White area might be from the Betadine, yes.
So that vet wanted $3,000 ? Or is that a typo ? If that's what they quoted you it's time to find another vet, an honest one. That little snip could be done for probably less than $300. You could do it at home with a sharp, sterile pair of scissors. It would bleed a little , you'd clean it off and put raw honey or non pain-relief type neosporin on it. Wrap with a little gauze and it would be fine. But I understand that most people prefer the vet to do it.