If all else fails, feel free to send it to me. My three-year-old DGD absolutely LUVS to pull "fuzz" off of stuff. She practically denudes anything I make for her!
It started when she was a baby. I made her several crochet blankets and she always had to have one to go to sleep. Apparently, she'd pull at it until fuzz came off, hold the fuzz in her right hand, stick her left thumb in her mouth and fall asleep immediately. No blankie (i.e., no fuzz), no sleepy! Drove her Mom nuts!! (Must say I secretly loved it...my baby loves her Nana's gifts!!).
Anyway, as I said...if all else fails, feel free to send it to me. I'll bet she'll have it stripped bare of any "fuzzies" in no time.