I do the same as you with the disks and never remove the bark.
The bark on cherry wood is kinda tough and stringy, in bands that go around the wood. Which can make the wood a bit difficult to split, especially in rounds bucked for firewood.
When I buck cherry wood I always score the bark from one end to the other, and split it at the score. It'll split easily that way.
We get a lot of wild cherry that grows from suckers and they make great smokewood. Its one of my favorite smoke woods because its easy to get and adds a nice flavor and color to whatever you cook or smoke with it. When I burn it in the stove my neighbor asks what I'm cooking.