Out of all the natural, aluminum-free options I've tried, I like Truly's All-natural deodorant(1): it smells nice (light coconut smell), lasts all day, and noticeably reduces perspiration. I've been using it for more than two years and have no complaints, other than that applying it is slower than the stick-based deodorants.

Definitely worth a try.

[1]: https://www.amazon.com/Trulys-Natural-Lasting-Organic-Deodor...

If you use an anti-fungal soap a couple times a week it helps, e.g.:

https://www.amazon.com/Antifungal-Athletes-Toenails-Deodoriz...

https://www.amazon.com/ArtNaturals-Essential-Peppermint-Euca...

> non-aluminum based deodorant/anti-perspirant

Are there any non-aluminium based antiperspirants known?

Schmidts works pretty well if your skin doesn't react poorly to the Baking Soda in it.