It's gonna have an odor after you rub it all over your armpits!
Besides, I just can't see rubbing the alum block on your armpits and then proceed to rub it all over your face. Perhaps they're small enough that you could pack 2?
It's not gonna have an odor if you use it on your pits after you shower. I use the same block on my face and pits. I figure they are equally clean after a shower....I think an alum block is better than any antiperspirant/deodorant that I have used. I used to get white stains on my dark blue uniforms in the armpits from deodorant/antiperspirant. I always thought it was salt from sweat....That problem went away when I started using alum.