Image credit goes to www.pissesmeoff.org for the box trap drawing.

Have you considered snares as well? They're smaller, cheaper and easier to store away or carry in a bug out bag. No idea if they're legal to use in your state in a non-emergency.

I know very little about snares --- just what I've seen on Survivorman back when we still watched Netflix. I suspect they might be less safe with pets?

Studies have been done by many of the states regarding domestic dogs and snares. Dogs, especially those broke to the leash and a collar simply sit down after being caught and are alive and well when you arrive. A snare set for a coyote will typically be too high for a cat; it will walk under the snare and never be caught. Same thing for a snare set for raccoons and dogs.

If you're worried about pets they make a relaxing locking mechanism that will relax as soon as the animal stops struggling. Many states such (I think Missouri, Pennsylvania and Wisconsin .. off the top of my head) only allow these relaxing locked snares, they're called cable restraints, to be used. They release domestic animals unharmed frequently.

The veteran snareman is able to set their snares to target a specific species and not harm others.

If I was more desperate, those techniques would probably sound pretty good. But right now, I'd rather shoot a deer than risk that our ultra-skittish cat would figure out to stop struggling in a snare....