You are not understanding what you are watching. Those are not chopping moves, they are cuts. There are some very important differences. If you use your cane the same way, you would not be doing the amount of damage your cane should be doing, because you would be cutting with it.
What little I know about katana (and I stress, what little I know) I learned from this guy: (if you know where to look, I am in one of the pictures with him) He helped my set up my DZR school, and the last years of his life, we taught at the same dojo...
If you want to learn how to use a cane... learn to use a hanbo. It will teach you a lot of different ways to use a short stick or cane.... both to strike and to grapple.... both at distance and up close.