Welcome to the world of trapping cats.
When trapping cats in the desert country, I do everything possible to not catch skunks, but the only thing I've found to pretty much assure the least amount of skunk catches in cats sets is use urine only. This isn't fool proof, but I don't seem to catch many skunks.
If you are using a food lure or any scent that has a skunk essence in it, it attracts skunks. I usually set 2 and sometimes 3 traps in a good cat location so if I do catch a non-target animal, I still have a chance for a cat. I realize that this isn't always possible if you don't have a lot of traps, but I have caught many cats in locations where I had 2 or more traps set and had a skunk in the other. I figure the skunk just helps lure the cat into the area better.
I once caught a big tom who had a huge belly on him, like he ate 20 lbs of something. Being the curious type, after skinning out the cat, I cut open the carcass and found he had caught a skunk and ate it. This didn't deter him from working a urine set I had set for cats though.
Skunks are just part of running a cat line.