In NY, it is illegal to relocate wild animals as that can spread disease. In addition, if I don't want the darn thing around, I figure no one else does either. Also, there is no shortage of these animals, so if you try to relocate it, you are just going to displace another one.
As a result, I have concluded to "Just have the guts to do what has to be done and dispatch it".
Woodchucks are the worst! They multiply fast, will go over a fence or dig under a fence, and will wipe out your whole garden in a few hours. The electric fence seems like the only effective deterrent for them.
One time I did have to eradicate one with the 22 from my deck. I did it on the 4th of July and no one noticed!