Catching a skunk isn't nearly bad as you think.
You just walk up to it quietly with a sheet or something to cover the trap and you can move it anywhere, or just open the trap and let it go.
Your other option is to keep the trap set from morning until just before dusk. I've had great luck with that. Make sure you bring him far enough away, so that he cannot find his way home. At least five miles, I would say.
Option three is the less humane... gas the little rodent.
Relocating it to another local might bring this unfortunate guest upon another and that's just not nice.
It also might be illegal in NH, so check on that.
Good luck! Let us know how you make out.
Cel