I mean adding antioxidants to soap formulation which can help create smoother skin and minimize common skin issues. such as vitamin E or etc
Sorry, it doesn't make much sense. I am not aware of any direct connections between antioxidants and skin condition. The only connection I know is they are both used in a typical mixture of buzz words used in marketing, but it hardly translates into practical and viable application.
That's not to say there are no substances that are valid and helpful components in the soap formulations, but in general - per forum rules
- we don't help in self medication nor in preparation of cosmetics.