I haven't used "deodorant" in years. Instead I use anti diaper rash baby powder, such as Caldesene, which is a mix of zinc oxide (which is antibacterial) power and talcum powder which promotes dryness (as does corn starch except bacterial feed on corn starch).

It works much better than anything I've tried which is marketed as deodorant (even the natural stuff which typically includes zinc oxide) and it's much more amenable to using on the whole body than that slimy stuff they sell as deodorant in the stores.