A little more on this. I have drilled out 5 wooden spools with slightly narrow diameters. I have wound thread on 2 so far. You may wonder how to make the thread stay on the spool when you begin winding.
I found nothing on this, in my research. So I had to experiment on my own. I started with the simplest thing; I just taped the end onto the spool. As long as the tape lays smoothly, it will wind neatly.