How do I make cotton wool stay on something?
“Glue gun” glue will work well. But be careful just to stick the balls together somewhat lightly–don’t “press” hard since you could press all the way to the glue area while it’s still hot and make a dimple in your cotton ball(s). Instead of gluing them together, you can also glue them individually to another surface (e.g., some kind of tight skull cap as a wig “base”) from their bottoms only…that way you can press them together as much as you want without deforming. You could also use a tacky white glue which will grab faster than glue sticks or regular white glues, etc., but the glue gun will give almost immediate hold.