I've had other chairs/wheels that could easily be taken apart. I think these could be if you had a special tool just for it, there was a snap type thing that I did take a screw driver too but it wasn't working. The chair in question (from Ikea) didn't just have a single ball, it had two wheels on either side of each foot. To make matters worse is that it wasn't like a vacuum cleaner when it gets tangled with long threads where they all go the same direction, from the scooting in/out the same pieces of dental floss would go around one direction and then the other direction. Absolute nightmare... I suppose I could be neater or I'm just going to try to be more timely!
Edit: I have an old oak wheeled chair, probably from about the early 50s. For that one I just changed out the wheels entirely, the old bakelite or whatever it was had broken chunks out of it. That was pretty easy, but these modern things are designed to be replaced and not repaired.