Cats are extremely tough for some reason. With a 22 lr I would stick to head shots. I have had extremely good shots on the vitals with a very accurate rifle and seen them flop a bit and run off. Would see the same cat a few months later. I switched to only head shots and solved the problem. I do still use centerfires on body shots out far, but they are varmint bullets. I use box traps as well. I run them near a creek and dispatch them in it. I use shad for bait. They are netted and frozen. Stink to high heaven but effective.
I have the same problem as you. No neighbors within a few miles so they are totally feral. They become very wary so just because you see them all around don't make the same mistake I did and think you can pop one whenever you want. A more stealthy approach is advised. Thankfully I have never caught a skunk. Only opposum and cat with the fish. I would advise you to devise a system to secure your box traps. I use aircraft cable to trees. It will stop the more honest people from walking off with them. Before I started doing this I lost quite a few over the years in places where no one was supposed to be.
Blessings