I wonder if it would be possible to spin the mouse around enough to make it dizzy before launch, then it would swim in circles increasing the chances of utilization??

A very gentle catapult seems to be the easiest way to launch the mouse without physical harm. Variances in the body mass will affect distance obviously, but a mean body mass could be used to reach the mid point of the body of water, allowing lighter specimens to travel farther, and heavier specimens to land nearer to said launch mechanism.