Ditto Benjamin. The only time I need deodorant is if I start using it.
That is to say that if I start putting on deodorant regularly, I start to stink when I'm not wearing it. (I am 6', 185, with plenty o' hair.) I don't suffer from B-O, (confirmed by my girlfriend of 3 years,) and I avoid deodorant like the plague. I think my current stick is a year old.
Just like those acne creams that give teenagers temporary relief but dry their skin out so that the next breakout is worse. I think deodorant is a scam.
Try going without for a month and see for yourself. Shower every day and wear clean clothes, of course.
To combat a showerless week of hiking, shave your pits. No one will know, it's more comfortable, and you won't have those knock-yourself-out moments in the sleeping bag.
In fact, your pits aren't the only thing worth shaving. Hair holds in sweat and is a great place for stink bacteria to grow. Get yourself a fresh razor and go to town; by day 5 of your next hike you'll thank me!