I have the lumps in my pits too, I also have HS. Some docs told me not to use anti persperant, some said it made no difference. I feel that I really do need to use it as I would say I sweat perhaps slightly more than average I guess.
I also use the Mitchum that Hvns uses, and I swear by it, its fantastic stuff, I use the roll and as Hvns said, it really does what it says on the tin ! One application until your next wash and no nasty wiffs at all !! I find that anti persperants dont effect my HS at all, altho obviously I dont apply them to an open wound.
I have recently tried the Dove solid stick anti persperant without any problems too. I love the Dove range ! Also using the cleansing bar, it doesnt leave that horrible 'tightness' that soaps do.