I used to be concerned about aluminium in antiperspirants because I heard rumours that they were carcinogenic. But I've been researching it again recently, and there appears to be no scientific basis for this rumour.

So if you are not concerned about aluminium in antiperspirants, you could try Certain Dri Roll-on Antiperspirant. Peta's website says that it's vegan, and it's supposed to reduce sweat significantly for most people. I just bought some yesterday and I haven't tried it myself yet, though. It has mostly very positive reviews on Amazon, at least.

Personally, I wish that society would relax a little about sweat and natural body odor. Nobody likes a stinky basement-dweller, but as long as you bathe regularly and wear clean clothes, a little natural deodorant should be more than enough. I know that some people you associate with might hold you to a higher (and ridiculous, in my opinion) standard though, so I understand why you might want to avoid having to deal with fussy people's judgements about how much sweat your body happens to produce.