There was a great PBS commercial last year. It had a skunk walk into a house past people through the kitchen, up the stairs, into the bed. Then the camera focuses past the sleeping man in the bed and on the nightstand is a photo of the family with their pet skunk. It's message was that PBS thinks outside the box.
Ironjerry got it right.
If you don't have a place to teach him to swim. Cover the cage and spray him with ether or you can gas him with car exhaust. Do not relocate him somewhere else! In most states that is illegal.
I would take it to the far back end of your property and shoot it. Or use a big trash can filled with water and drown it. I wouldn't try to let it out of the trap live, you might get hurt. And you can't relocated it outside your property unless it's legal in your area (which is unlikely).
If animal control serves your area (it doesn't serve mine), you can call them and maybe they'll dipose of it however they do it.
If you are going to dispose of it permanently then shoot it or crack it over the head really hard to kill instantly....any other method is just inhumane -
I've never had a cat mess with my chickens so we don't pay the strays any attention. BB gun in the butt usually keeps them from ever coming back to even get the chance to think about food here. Plus, we have dogs who love nothing better than to chase a cat off.