Try contacting your local Wildlife department and see if they can help. Other than that you might try to bait the cat then shoot it when it comes too eat. I don't know if this works with cats or if it is legal in your area but it has been known to work in our area on problem coyotes.
Best of Luck!!
Ditto on checking with the wildlife department. They should have good advice on how to accomplish the feat. More importantly, if you do it the wrong way you could find yourself seriously afoul of the law.
Over the years I have seen several elk and deer hides left in the woods by hunters and I have to wonder why they do this? I fully understand and agree about getting the hide off the animal as soon as possible to cool the meat, but why not pack out the hide with you and use it? As far as I know there are no state laws that require you to take the hide home, but to me why waste such a beautiful part of the animal? Some might think they have no use for the hide or it costs too much to tan....