Something that might work (we used to do this for training dogs to flush quail) if you really don't want to stun it, is to put it in a bag, spin the bag around quickly enough to get the mouse dizzy/disoriented, then quickly put him back in the cage. It works well enough on quail to stop them wandering off, so fingers crossed it will disorient a mouse enough to let your guy grab it. Just a thought.