Uhm. "Killing the original mouse" is not inherently inhumane. The standard technique for "sacrificing" a lab mouse snaps its neck about as gently and suddenly as one could reasonably expect; death is rapid and fear/pain are believed to be minimal.
Probably more humane than your last meat meal.
There are working animals, there are lab animals, there are food animals, there are companion animals, there are zoo animals, there are wild animals. The same species -- and indeed the same breed -- may occupy any combination of these. "Humane" involves causing the individual animal minimal discomfort (physical or psychological) given the role we are asking it to play. If you want to object to some of the roles as inherently inhumane, that's a different conversation.