Your route sounds pretty safe to me, but I do think you could do some pruning of the long thick branches (trunks) with no problem. You can wait till the tree starts to move buds to do this, at the time you repot, but not after leaves open. Cherry trees are hardy and fast growing as you may know, so if the tree is in good health, I would not worry about doing the rootwork you are planning. I use a coarse drainage layer at the bottom of the pot for cherry and also put in a deeper pot than I would use for other trees.