I'm wondering why you should need a hunting permit to put down stray or feral cats?
If they are on your property and causing problems, you should have the right to shoot them.
I don't support the idea of a hunting license for cats, because I don't think you should be shooting cats on someone else's property, unless specifically asked to do so.
I also think that it it has a collar, or you know it's someone's pet, you shouldn't be shooting it. If someone's pet is causing you problems, but isn't an immediate danger, call animal control and let them deal with it.
"I don't support the idea of a hunting license for cats"