I often get asked about using a 4.5mm Steel BB gun for pest control and to be honest I really don't think a BB gun is the right tool even at close range to properly and humanly take care of pests when need be. A much better tool is a high powered pellet rifle in just about any caliber as long as you have taken the time to practice your shot placement at a variety of ranges.
Read full article here:
https://www.replicaairguns.com/2014/9/6/bb-guns-shooting-at-longer-ranges.html
Buy the Umarex Steel Force in Canada:
http://www.replicaairguns.ca/umarex-steel-force-air-rifle.html