More efficient? Most likely. As much fun ( since you have to dispatch them anyway ) ? Nah !A few dozen 220 conibears and be done with it. Shooting them is too time consuming to get good results.
Find the holes and stake the 220 right over it. Come back daily to remove the 'chucks and reset. Daily checks are the key. Nothing nastier than a bloated woodchuck covered in maggots.