I would stick with 40 yards and under for the shotgun. I found that my Win 1300D patterns pretty decent at that range without using a choke at all (haven't had one installed yet), and though yours will pattern differently, I'm sure you'd get better choking than I do.

You might also want to carry a .22LR pistol or rifle with you as well. That way if you have to finish it off, you won't waste the ammo nor absolutely ruin the animal... unless you just absolutely HATE the buggers and would rather use your shotgun at point blank range.