Yes, that sounds fine. Much more humane. Carry on.
As long as the ethics committee OKs it.
As to possible alternative methods, those include freezing, which could be quite prolonged and painful, and blunt force trauma, which could be difficult/ambiguous to perform correctly and confirm correctness every time.
My daughter did say it's done so fast and the mice are so accustomed to being handled there doesn't appear to be any fear on the mouse's part and there doesn't appear to be any suffering, let alone needless suffering.
Funny anecdote - the first time she was in the lab when they were doing this she hadn't had breakfast that day and had a light dinner the night before and she fainted from low blood sugar. Took her a couple of days to convince them no, she was fine, she just let her blood sugar get too low.
Given that its the case, you then wonder about the most effective means of killing them.
But, pushing back on your assumption, what value can there possibly be in killing baby mice?
I expect I don't need to explain why it's best to kill the mice humanely for medical research which involve dissection of some sort.
For snake food, it's best to feed mice that have been euthanized. Feeding live mice is cruel to the mice, who experience terror right before death, and there is also the possibility that a struggling mice could injure the snake.