Hi Sarah,
Once we’ve made sure it’s matted fur, then removal is the appropriate step to take. Hyperthyroidism is not known to cause thinning of the skin so there could be other medical issues. There are some drugs out there that might cause a mild sedation without affecting systems like the heart, lungs, or kidneys. You should talk to your vet about options and they should best be able to help you including the clipping.
All the best,
Dr. Ryan Llera