Randy Savage had several large cowboy hats during his baby face runs.
The Undertaker's entire persona would be a lot less creepy and intimidating if it weren't for his Badass Longcoat and trademark wide-brimmed hat together making him look like a gigantic psychotic Amish gravedigger. Also the bandanas that he wore as Biker Taker. He even color-coded them to an extent— when he was wearing red, he was in full-blown heel mode, while black/dark blue generally were for his face persona, although the rule wasn't absolute.
Hillbilly Jim's straw hat, although he can be seen wearing baseball caps these days.
Mr. Fuji was famous for the bowler hat he wore as a manager until 1993 and which gave him a look that drew comparisons to the character Oddjob from the James Bond movie Goldfinger, played by wrestler/actor Harold Sakata, and, like Oddjob, Fuji also qualifies for Badass in a Nice Suit.