I would say yes you can, because i breed mice and they always seem to have babies right before i clean, so i am forced to move the babies. I have never had mice or rats kill any babies after i have handled them, and i have had a lot of different mothers and litters. I am not saying you should, because it really all depends on how much your mouse seems to trust you. My mice trust me very well because they were born and raised here, so they are very used to me. I think it is pretty safe, but i am not guaranteeing anything. tell me if this helps!

Abby