The best thing I have found for pests such as mice and other very small critters and pests was a Crosman 760 pump up. They are not that strong on just a few pumps. I do not remember the number of pumps I used, it was based more on the size, how far, etc and I shot BB's.
At the time, I lived in a trailer (moble home) and the first time I was going to shoot one was with my Ruger target pistol, but thought the wife would not want a hole in the floor as it was going to do that. I had no doubt I was going to hit him, I was one heck of a shot back in the day with a pistol. We would go shooting and everyone would say "where is your gun" as everyone else brought rifles and were good shots. I could shoot anything with my pistol they could with a rifle, but that was a long time ago.
Anyhow, the mice, I made it into a "game". I would sit and watch TV after work and after eating.
I would sit on the right side of the couch, which had a straight shot of under the dinning room table. The rodents do not like to get out in the open, mostly you will see them along the wall. Either way, along the wall or under the table, that old 760 Crosman took them out with 1 BB to the head (I like head shots) and pumping it low, the BB did not go through the mouse and hit anything.
I miss that, BUT- NOT that I would want mice now, the 760 is gone, I am not the shot I was (I used to shot 100 rounds a day- Everyday, no matter what)
So, you may want to try a 760, you have power over the power it puts out so if you miss, there is not that much damage. After all those shots, I never did miss one that I can remember and no damage was ever done to the inside of our home, plus, it was great fun at the time as you watch TV, you could see movement out of the corner of your eye and then it was- GAME ON!!!