I think it's also predator/prey---I've seen documentaries on wild cats (bobcat/mountainlions) and the bob cat was hiding from the mountain lion because the mountain lion would eat the bob cat. So, probably the mountain lion pee would work, if you could get it safely....
"for people to just toss their cats outside and say its someone elses problem.. Its awful"---
This quote is what I very clearly said is cruel/criminal, you've misquoted me.
What size of trap would you use, where would you place it, and what to use as bait? I'm in a similar situation, but with a stray that seems to have been recently dumped, so that might be more similar to the OP than for a feral cat.