Ahhh, bless you, Darcy, you are an angel.
Could you coordinate with the lady who is trying to help the raccoons, i.e., if you catch one give her a call? If you could put the trap on, say, a sturdy table or something else too high for a skunk to climb onto, that would take one species out of the mix for trapping purposes. I have been surprised at some things that skunks can climb, but they aren't real adept at jumping.
Raccoons don't jump well either, but they sure can climb and they are strong, so I don't know how easily you could set up a cat-accessible, raccoon-proof spot to set a trap. However, if you keep catching raccoons and their friend takes them, eventually you'll run out of raccoons and have only the cats to catch. That's the theory anyway.
Good luck! Head bumps and purrs to all.