I hadn't thought about a snare, but I might scrounge up some cable. The big problem is getting turned in by bleeding-heart neighbors. I'd just as soon the groundhog moved to THEIR houses, instead.
A buddy is president of his condo association. He said they trap groundhogs by using moist cat food as bait. The problem becomes, what do you do with a grumpy groundhog? He said he could come over and "screen" me while I popped the critter. I have some .22 BB caps that are about as noisy as a pellet gun, and a nice S&W .22 revolver to shoot it in.
Neighbors need to go too sounds like to me.