They can't bring themselves to use the trap? I'm really confused on that one? Why in the world not? Anyways, the right way to do this is to get a live trap from somewhere and cover it somehow. I wired cardboard to mine. You also have to rig something up so that you can open the door without allowing the skunk to see you. I used wire again here. I wouldn't bother with putting cardboard over the ends, just the long sides and the top.

Now go trap your skunks, carry the live trap away (and by away I mean a really dang long ways away, like a mile from any residence. I put the trap on a trailer behind the pickup and drove away). Open the cage to let the skunk out. Wait for it to come out. Shoot it. Make sure you're standing upwind first.

If they can't see you, they don't spray you. At least that's been my experience. Just don't let them see you during the entire process until you're ready to end their lives and you're a long ways upwind (and make sure the cage is upwind as well). Make sure you have a weapon that can get them at a distance. I used a shotgun. Who cares if it makes a mess of them. I'm not planning on keeping the hide.