I've never had groundhog so take this as me simply passing on what I have head from others.
I know some folks who eat them and enjoy them. In fact my Dad was what most folks would think of as a hill;billy coal miner's kid who came out of the hills for WWII and never went back. He grew up eating them and the old family recipes had a number of ways to prepare them.
As we've discussed amongst some of us here in farm country they are the largest member of the squirrel family and eat the same things that deer, turkeys and other wildlife do so what's the difference?
The general opinion is that if the critter is young enough to have smooth soft fur and teeth that aren't yellowed they are tender and good eating. I suspect that you could to worse than to hit the critter with some rub and chuck it in the smoker. Let the results point you to the best way.
Good luck and hopefully some more with experience closer than one generation removed comes along.
Don't worry about "cruel". The darn things can kill a lot of young corn and eat an awfully big patch in a soybean field. I'll be shooting or trapping every one I see....