Can I Use Equate Povidone Iodine Solution on a 10 Week Old Kitten?

No, it's not safe for cats as they will lick it off their fur. Iodine was not meant to be ingested. What you need is an anti-fungal shampoo, ideally from the vet (he's due for vaccines anyway). If you won't take him to the vet, then the pet stores sell ringworm shampoos - be sure the one you buy states it is safe for cats not all are. Bathe him every three two five days, and twice a day put a thin film of Lamisole cream (in the pharmacy with the athlete's foot preparations) on each of the lesions twice a day. It's going to take at least two weeks probably longer until it's gone, and in the meantime he's potentially contagious to you. If you have small children they will surely get it from him - ringwormm is a disease of the young and immune-suppressed.