I love all of these non-trappers that give trapping advice, lol. Drowning is not a inhumane way to kill, in fact, the BMPs (Best Management Practices) agree that drowning is a very humane way to kill trapped animals.
However, although plenty of fox have been caught in cage traps, the odds are against it. Is there no way you could keep your cats in the house or barn for a few days? If it was a coyote, I could suggest tightening pan tension to avoid your cats, but red fox and cats are similar in weight, so if you adjusted the tension to guarantee not catching a cat, you'd likely miss the fox as well. You could try using a fruity bait, such as watermelon (which fox and coyote love and cat's don't) but there's still always a chance your cat would stumble into the trap accidentally. If you used a #1.5 coilspring, you could release your cat unharmed, although his foot might be sore for a few days. I'd reccommend caging the cats until you catch it in a foot trap, because if he gets a chance he wont turn down a cat dinner either.