We feed outside cats and I've unfortunately caught many varieties in live traps...raccoons, possums, feral cats and even skunks. Everyone apparently loves Special Kitty Dry...thank God it's cheap. We take the cat's bowl in at night and leave a small bowl in the live trap. Most of our cats learned after being trapped once. One really dumb one was trapped three times before figuring it out. My dispatch method involves a shovel and a hole in my field. I don't want any of these pests coming back.
...and I'd quit feeding the cats, but they do provide some rodent control benefits. The trick is to not overfeed them so they get fat abnd lazy.