Deodorant & Antiperspirant
Antiperspirant: A product which reduces perspiration (sweat) at the site where applied.
Antiperspirants directly affect the function and structure of the body by reducing the perspiration at the site. If you make a product that claims to reduce the amount of sweat, the product is a drug.
A product that reduces sweat AND changes the smell would still be considered a drug.
Deodorants
Deodorants, if they only reduce or cover odors (smells) don’t actually change the function or structure of the body; they change the smell of the perspiration AFTER it has been produced by the body.
If you make a product that only claims to reduce or change the body’s smell, the product is a cosmetic. There are no restrictions on the ingredients that may be used. All cosmetic regulations apply.
OTC Antiperspirants
While antiperspirants may look like cosmetics, they are over-the-counter drugs. In order to be marketed as antiperspirants, products must meet the OTC Monograph for antiperspirant products, using only approved ingredients, label claims, directions, and warning statements.
There may be natural substances which could be used to reduce perspiration. However, only products which meet all the requirements in the OTC monograph for antiperspirants may be promoted and sold for the purpose of reducing sweat or perspiration. The only approved ingredients are various forms of aluminum.
Also keep in mind that even if you could get the ingredients and make a product that meets the requirements, in order for the product to be legally marketed it must be manufactured in a facility that is registered as a drug manufacturer with the FDA1 and which follows drug good manufacturing practices as contained in federal regulations.2 It is likely there are state-level drug manufacturing registration and licensing requirements.
1 21 CFR 330.1(b)
2 21 CFR 330.1(a)