This assumes you are using a Hav-a-Hrt or similar live catch trap.
Pick up a small tarp or poncho, and hold it in front of you. Very slowly and carefully walk towards the trap, then slowly lay the parp over the trap. You might need to cut a slit in the tarp so you can get to the handle of the trap. Then carry the trap to where ever you want to release the skunk, you can even load it carefully into a pickup bed. To release the skunk, you can tie a rope to the door. Hit the release, and slide a stick or something under the door, so it doesn't latch. Then you can pull the rope and open the door from a distance. You will probably need to leave the door open for several minutes before the skunk will emerge, although sometimes they come out quickly.
My company does a lot of nuisance animal trapping, and this is the method my techs use. The only person ever sprayed was a friend who trapped a skunk at his parents house. He picked up a large tarp to cover the trap, and tripped over it. He fell with his face about four feet from the trap, and the skunk let him have it, right in the face! He like to have never lived it down!