Throw a tarp over the cage. Use a tarp that you are willing to throw in the garbage afterwards. Then you will be able to pick up the cage with a pitchfork or hoe to dispose of the skunk as you wish.
Remember that skunks are very good at finding their way back home again. So don't think that if you drive that skunk 10 miles from your house that it won't show up again. I avail myself of the local wildlife dept program, don't know / care what they do with the animal. I have a neighbor who prefers to teach them to swim in the local lake, with a little added ballast. Tie a rope to the cage first if you decide to do that.
Also, look around for a litter of babies. Females may be nesting in your area and those babies will need to be humanely taken care of as well. I find it best to let the wildlife dept deal with the babies.
Lastly, try to prevent skunks from happening again. Close up all holes and entry points (I fill them in with concrete), liberally sprinkle moth balls under porches, sheds, etc..., and keep the area moist when all else fails. Skunks dont like to nest where it's wet. That's another good way to ferret them out from under something...stick the end of a hose down an entry hole and turn on the water full blast. Even after they come out, leave it running to really wet the place down, throw moth balls in there, fill up the holes, and pray they find another home.