I've caught dozens of skunks over the last several decades, some accidentally. I used to be terrified and released them without moving the trap. When I was about 12 I learned not to shoot them. Now take them down to the little pond behind the barn and give them scuba diving lessons. I haven't found any little diving masks to fit them so none have signed up for repeat lessons.
I made a sled from a piece of sheet metal, turned up on the leading edge. A rope is attached to the front. I approach the trap holding a small tarp in front of me and drape it over the trap - if the skunk can't see a clear target it won't spray. I use a pole with a hook (leg crook) to pull the trap onto the sled then hold both ropes and slide the combo to and into the pond. I've dragged traps about 1/4 mile like this with no problems. The only thing that ever went wrong was with the trap with three skunks. After about 5 minutes under the water I pulled the trap out and dumped the contents on the ground before heading back for the second skunked trap. When I got back one was gone! While puzzling about this I noticed one of the remaining two was barely but still breathing. Maybe the first one did some CPR before running off. Since then skunks get a longer swim. In fact, I was so upset when the big skunk killed and ate the young female peacock I left it in the water for 30 minutes and then did some 22 rifle target practice with its head as a target. I figured if it survived after all that it deserved to eat peacock for supper.
A pro varmint guy who will come to your house and remove skunks said he covers traps with cloth and submerges them in a 55-gal drum full of water. I've used this method on animals for the vet students to dissect and study keep from destroying tissue. For other animals that simply have to be put down due to severe medical problems I use gas.
Just to be clear, I very much dislike killing anything, chickens to eat or predators who eat them before I can, even mice and rats. I'd hate to be like my friend's son who always killed the hogs we put in the freezer - once when walking out with a 22 rifle he said "I just love killin' things - it's my favorite thing to do!" Yikes. I worry about that boy.
JKJ