I don't have the heart to use lethal traps, either, but hubby doesn't like mice in the garage.
So I trap them in live traps and transport them (or have him
transport them) to the end of the drive and release them. And yes, I know they probably beat me back to the garage before I've reached the house, but it makes hubby happy thinking they're finding a new home somewhere else!
And if a 'new' mouse moves in overnight, well, I guess we'll just have to put the live traps out again and take care of 'that one', too!