Basic Trope: A character is notable for their refusal to use guns.
Straight: Bob is a professional killer who has absolutely no remorse when it comes to taking someone's life. However, he absolutely refuses to use guns in his line of work.
Bob is an ego-maniacal dictator who's trying to take over a country, but refuses to use a gun and doesn't allow his soldiers to carry them either.
Bob, a crazed dictator, is enraged if he sees someone so much as holding a water gun.
Downplayed: Bob is a technical pacifist, and swears off all lethal weapons, and even most of the semi-lethal ones.
Bob prefers to use his hands or knives, as guns are noisy compared to those methods.
Bob has Super Senses and can't stand the sound of gunfire or the smell of gunpowder, and walking around with earplugs and a gas mask would be suicide in an environment where it's important to avoid being snuck up on (not to mention opening him up to all the reasons you shouldn't hide the hero's face).
Carol, Bob's daughter, was killed when a gun he was handling accidentally went off. This scarred Bob for life.
Bob is an Actual Pacifist: a weapon in general would not fit with his ethos.
Bob thinks he has bad aim (which may or may not be true) and feels that giving him a gun is sure to fail.
Bob is completely helpless without his gun. When he's disarmed, he's toast.
Bob uses a gun to be more humane than his opponents who cause horrible deaths with toxic weaponry.
Bob seems like the kind of guy who would refuse to carry a gun... but he does.
Bob pretends to hate guns so that people think he's unarmed. He carries a hidden gun with him at all times.
Defied: "I may not like the use of guns, but anything that people are gonna throw at me is something I've got to throw back."
Discussed: "I swear, every time someone I know dies in a fight it's a gunshot wound. Most people in my place would've started avoiding guns by now. I mean, if that one book I read is anything to go by."
Conversed: "So...he doesn't have a problem killing people, but he has a problem using a gun? Interesting."
Implied: Bob looks at a Wall of Weapons, and seems to be disgusted at the guns, settling instead for a Katana.
Bob doesn't use guns and that's noble. Unfortunately, the people he faces aren't so noble and they shoot him down.
Alternatively, Bob is forced to use a gun - which causes him great distress, and he misaims, shooting the wrong person.
Bob refuses to use guns, so he finds other ways to disable his opponents.