Could you cover the ball with a piece of fabric? Essentially, like, a scalp. And you could punch holes in the fabric and thread the yard through for hair, before attaching the fabric to the ball. You could pretty easily secure the yard on the underside of the fabric with tape or glue.

Also, I would maybe "unwind" each strand of yarn if you really have some time on your hands, so it's more like hair then big pieces of yarn.
"I don't know! I don't know why I did it, I don't know why I enjoyed it, and I don't know why I'll do it again!" -BART SIMPSON