You can get devices which use sound to scare them off these days. I am about to get something and like yourself, dont want to kill.
Mice have excellent homing heads, you have to take them miles to let them go, or they find their way back.
The shops and restraunts bellow my flat and the many single folk/ students in the area keep them going.
The only true way is not to leave any food/ crumbs for them and they will go elsewhere.
I am in the situation at the moment where I need to do something though.
We had a rat in the back garden which was sustained by the bird feeder on a tree.
cheers