I have an old rug that I cover the trap with and then carefully carry it away from the farm buildings......then I shoot it and let the smell cool down for a day or so and then empty the trap.
We have a big long rope attached to our trap so we can drag it without getting close for situations like this. I think your only option at this point is to get sprayed or shoot it from a distance (hopefully it is situated somewhere you can?). Sorry
I've watched that guy "Billy the Exterminator". He has a show about all kinds of problems like roaches, bees, coons, snakes....all kinds of pests that can cause problems for people.
Anyhow, he traps those skunks in a live trap, and he will just throw a cover over the trap, and then he relocates them. He holds this planket (or whatever) up like a shield when he releases the varmit.....