Except now you’ve got a bunch of slimy mice.
In the winter, mice tend to come into my house for refuge from the cold, despite the many cats we have. This past winter, there were 5 mice captured that I know of. Two did not fare well … the cats found them before I did. One, the cats found but I managed to wrestle it away from them before they did any bodily harm. The other two, we caught in plastic live-catch mousetraps before the cats were even aware of them.
Of the survivors, I put them in a tupperware, drove a couple miles away, and released them on their own recognizance. For all I know, a hawk swooped down and ate them once I had my back turned, but I figure I gave them all a fighting chance.