Coursework that uses live animals is exceeding rare (unfortunately, IMO), so you should have very little trouble completing PhD coursework without using live animals
As to your research, this is an entirely different matter, but not all labs do in-vivo work. I suggest looking up faculty in the specific departments you are interested in, and seeing if there are enough labs that don't use mice to offer you a fair opportunity to land in a lab that doesn't.
Also, I recommend giving the animal work a try, possibly through a rotation. Some students really change their minds once they start doing animal work. This goes in both directions. Some students find it to be not so bad as they thought it was going to be, and others who really thought they were to have a career doing animal research just have no taste for it when they actually try it. Try not to let preconceived notions about how you will react dictate your research career. Find a way to expose yourself to it in a small amount, and see if you're right about how you actually will react.