In various media, con artists and other crooks who pride themselves on their wits tend to dislike using guns. Usually, they also dislike carrying them; sometimes, they don't want to be anywhere near them.
It might be simple fear because guns are dangerous weapons and the conman might very easily prove to be far less proficient in a gunfight than his supposed victim. It may be pragmatism, as guns are often taken as evidence of intent to kill and will usually get you a longer prison sentence if you get caught, as well as increasing the chance that someone will draw a gun on you in return. On the other hand, it is quite often a point of pride — guns are beneath them. After all, they aren't called the conartist for nothing — a truly good conman makes people do his bidding with cunning. Just threatening to shoot somebody is inelegant, if not outright cheating.
From an out-of-universe standpoint, it's usually because the easiest way to turn a Loveable Rogue, The Family for the Whole Family, or The Pirates Who Don't Do Anything into terrifying, evil criminals is to show them terrorising people with guns.
If guns have not been invented, then sometimes the con artist will have a dislike for swords, or knives, or whatever else is the most prolific/dangerous personal weapon.
Arsène Lupin's grandson Lupin III. The difference with his ancestor is that the latter does carry a gun, because for someone in his position not having one is just stupid.
Also subverted because Lupin regularly travels with a man who is explicitly one of the — if not the — greatest gunslingers alive.
The English conman/sorcerer John Constantine from Hellblazer hates using guns, and will tend to use wits and magic even in the most direst of situation. This was later changed in the movie adaptation, where John is a gun-totting American exorcist.
Films — Live-Action
The main character in the film Matchstick Men keeps a gun next to his money. When someone tries to rob him, he doesn't want to use it.
Played with in Maverick. Bret Maverick is a great conman and supernaturally quick on the draw, but he only shoots one person in the movie. The rest of the time, he's shooting objects (guns in hands, rocks above a criminal's head) or just intimidating people with his skills.
None of the cons in the Ocean's Eleven films like to use guns. The only time they do is when they're impersonating a SWAT team. In the third film, Linus gets more offended by Toulour threatening him with a gun than with ripping him off. However, the gun turns out to be empty, and the diamonds he takes were fakes anyway.
In The Flim-Flam Man, the rather elderly conman Mordecai Jones (George C. Scott) never uses force and surrenders peacefully when a gun is pulled on him.
Surprisingly averted in The Sting as main character Hooker would happily kill the villain in revenge for the murder of his friend Luther, but realizes that he doesn't know enough about killing people to successfully pull it off and opts for cheating him out of a fortune instead.
Mick Connelly in Betrayal in Death is a con man, pick pocket, and various other thievery-related professions. He expresses a disdain for the guns in Roarke's private weapon collection, instead perusing the knives.
Moist Von Lipwig in Going Postal dislikes swords because they "raise the stakes too high". In Making Money, he buys a cosh because life's too dull and he wants to raise the stakes a little, and immediately wonders what he was thinking. Vetinari also calls him on this, marveling what Lipwig "who has never struck a man" would want a weapon for. In Going Postal, Lipwig himself takes some pride in his non-violent nature and is offended when his golem parole officer calculates he has "killed 2.338 people" by ruining people and hastening the deaths of many by just a bit. At the end of Making Money, Vetinari experimentally shows that Lipwig dislikes weapons so much he is more nervous when holding a sword than when being threatened by one.
On another note, the Thieves' Guild prefers to incapacitate or frighten its victims into handing over their possessions rather than killing them outright, because that would intrude on another Guild's territory (the Assassins' Guild). Reducing the number of people there are to rob in a city is also bad for their business. Of course, they are free to punish those who steal without a license however they wish. Thieves breaking demarcation by killing people earn a short word from an Assassin: "Goodbye."
James "Slippery Jim" diGriz, the main character and con man from The Stainless Steel Rat series is a variant of this. He sometimes carries a .75 caliber recoilless handgun with explosive rounds; however he hates killing, only using the gun to Shoot Out the Lock and related things. He also carries it in the shower.
The villainous triumvirate in the Hand Of Thrawn duology has one character who never makes threats or so much as touches a blaster, and that's the professional con man/actor. Then again, he usually gets on okay with the strategist, who is a clone of a Red Guard and is much more wiling to try violence. The politician once tries pulling a blaster on the strategist and is disarmed quickly enough that the strategist didn't even take the threat seriously; the con man probably remembered that the strategist is ridiculously good at combat.
Inverted with The Gentleman Bastards. In their society, not carrying a weapon would just be weird, so not only do they carry the traditional concealed weaponry of thieves, they must also carry more obvious weaponry to complete their cover identities. A Royal Rapier, for instance.
In Time Scout, Skeeter Jackson doesn't hate guns so much as he'd prefer a weapon he's more familiar with, like a Mongolian recurve bow.
Jack from the Dragonback books, like his uncle, never carries any lethal weapon. After all, they can't accuse you of assault with a deadly weapon if you don't own one. He does, however, enthusiastically embrace nonlethal weapons such as tanglers.
In Lawrence Block's Bernie Rhodenbarr series, Bernie, a burglar and conman, fears guns, as he tends to picture them being used on him.
White Collar: Neal Caffrey is usually able to talk his way out of a situation and never has to use one. He does prove in one episode that not liking guns doesn't mean he can't be a very good shot with one, though.
Eliot from Leverage doesn't like guns, but explains it's only because they're too imprecise (this from the guy who could probably kill you in various unpleasant ways with a toothpick or something). His reasons vary from episode to episode, but the real reason he doesn't like them is that they take him back to a part of him he doesn't like. However in The Big Bang Job he does state that not liking guns doesn't mean he can't use them. He is even able to put most action movie heroes to shame with his over the top shootout.
The rest of the team is a more straight example, besides the pilot, none of them wield guns for the entirety of the series. However in the pilot, both Parker and Hardison bring guns to the meeting when they had been cheated and in their flashback Sophie and Nate shot each other.
In one season finale, a really ticked off Nate buys and practices using a gun, intending to shoot the mark. Everyone else on the team tries to persuade him not to.
From the way Patrick Jane drops the shotgun in The Mentalist episode "Red John's Footsteps," he doesn't like to use them — contrasting with the team of hardboiled cops he works with.
Averted in LOST: Sawyer is MORE than willing to use a gun. Although he had never used a gun until just before the crash, when he thought he was killing the man who had killed his parents.
In Warhammer Fantasy Roleplay, followers of Ranald, god of thieves and gamblers, also avoid violence when possible, both because it's crude and unprofessional and because murder is a premise of a competing god.
Averted with gambler and con artist Nick from Left 4 Dead 2, who is more than happy to pick up a gun. Justified, because it's the Zombie Apocalypse, and wit won't get him anywhere.
Played straight through backstory conversation as, when first picking up weapons, Nick will sometimes mention that it is illegal for him to hold a firearm; since constitutional rights do not apply to those who break federal laws, it's most likely Nick was caught trying to con someone, before becoming a con man who couldn't use guns.
Walter Hardy in The Spectacular Spider Man typically doesn't carry a gun. The key word is typically — as he gets older and slower, he resorts to carrying one... and killed Ben Parker with it. He is genuinely remorseful, and believes he deserves to stay in prison, even turning down the chance to escape in "Opening Night".
Truth in Television: Not only con-men but burglars and other "professional" criminals will not carry guns, because the prison sentence for possessing a gun during a crime is much greater than without one. Plus they really wouldn't use it anyway. Unless you actually are willing to kill someone, it is just false courage.
It's also a point of pride, especially for pickpockets. As some retired pickpockets have told reporters, any tough can threaten someone with a gun, but it takes skill to steal someone's wallet and not have them realize it's gone.
For burglars it's also a point of practicality. The vast majority don't try to break into a place that's occupied, thus rendering a gun redundant.
The infamous "You have inherited $50 million" and "I didn't place $36,119 in calls to the Ivory Coast" Nigerian scammers are almost wholly adverse to violence. This can put them at a disadvantage when they accidentally piss off legitimately violent & somewhat Ax Crazy groups like the Russian Mafia.
The Mafiya in Russia prefer knives to guns, unless they're expecting trouble, because carrying a knife is a lot easier to get away with.
Carrying a gun gives you little gain for a whole lot of potential hassle. What if someone notices you've got a gun? Normal people don't carry guns. Conning is all about appearing normal and legitimate. A gun simply doesn't mesh with that image.