The OP did say that the vet gave him / her the betadine to use on the cat's wound so I'm sure the cat was seen by a vet. The OP can try covering the betadine application area with vet wrap or gauze to keep the cat from licking. Open wounds do need to be treated to prevent infection. Cat saliva isn't exactly sterile
NO!! You need to use something that will not make kitty sick--they can reach their tail to groom and that can make them ill. Discuss with the vet before using anything to clean out a wound. Rule of thumb is to leave any wound alone as kitty will groom themselves. If it looks infected, take to the vet and let them tell you how to manage. If infected, it will get green and smell bad. Antibiotics will then be needed.
Wishing your kitty well!!!