I see mink fairly frequently as part of my work. They are out during the day a lot and not particularly weary. The weasels are not as apparent, but they seem to operate during the day a lot at well.
In my settings, the projectile is slowed greatly by going through the target. When hunting small stuff in situations like a barn, the pump BB gun was not pumped all the way up so had good killing power with penetrating things like tin used on side of barn. BB's ricocheted easily, pellets not...
You will not be shooting when critter is on the run. What I do is watch for where it peeps out of a whole and have weapon trained on that spot. If shooting in the open, do so when it is basically standing in place which they do a lot. Wear glasses.