As he is young this could be a big concern.
When you put him in the deli cup, (keep trying f/t until you can get live again) put it in a paper bag or make sure the enclosure and room is completely dark and quiet with no disturbances. Until you can get live, try a few tricks of the trade with the f/t. Dipping in chicken stock, making sure the mouse is warmed under a heat lamp for a bit, even braining if your up to it.
Good luck, and make sure it's dark!