Spinning the stick minigames - How to not destroy my palms?
Wear gloves. It's as simple as that, no really.
Just wear gloves, if you want to, wrap some bandages around your hand if you want to look like a Tekken character. Anything to cover up your hands should suffice.
If you don't want to do that I suggest you go the way of Tigress from Kung Fu Panda and hit trees all day long. If you want to you can wear some textured gloves to prevent your stick from slipping if that sometimes happens. Otherwise, you can just wait for your hands to become calloused and it wont hurt anymore.