Maybe a trap and relocate the GH 's ? Cage traps are less than $100 OR a cage trap and gangland style head shot with a gun you already have ? or a tub of water to drown the beasts .
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I can’t believe I’m actually going to say that gun is a perfect fit for something but I have to agree. It’s perfect for this. You will just have to get proficient enough for a headshot in .22 for sure. You can usually post up on a groundhog hole and wait them out and get pretty close. I killed one with a .22 Airacuda max. One in the head and it went nowhere.Why not the Umarex Komplete in .22; around $200.00. It uses 3600 psi Nitrogen cylinders. For the occasional use, it would make sense. The nitrogen cylinders are about $12.00 each, but like you said, you don't want to get into the sport, so just an occasional investment.