What I do to wind a center pull ball is, when I don't have my ball winder nearby, is to grab an empty TP tube, put a small tear in it to hold one end of the yarn, then wind the ball as normal. when I'm done, pull the tube out.
Wisdom is knowing what to do. Skill is how to do it. Virtue is getting it done.
That which does not kill you, isn't trying hard enough.