I have a powerful air rifle and a selection of shotguns, and if I wanted to take a chance on wounding that mink and possibly having it escape with me not knowing if it was dead, I'd use the air rifle. (Yours will not be in a trap to assure a head shot from short range....yours will be moving or free to run off if your shot placement is not perfect). If I wanted to assure myself of seeing it graveyard dead with one shot, I'd use a shotgun with #4 or larger lead shot. Remember, that shotgun isn't just one pellet. Depending on the gauge, it might be several dozen pellets all from one blast....lethal out to at least 30 yards or so. Which is why that shotgun would be my preference by a factor of at least 100 to 1. Just saying.