Deodorant's are for smelling nice.
Anti-perspirants clog the sweat glands and turn sweat into a sort of sticky gel in which sweat cannot be excreted. Drumming and anti-perspirant? Not a good idea.
As for the doctor thing, I was under the impression some anti-perspirants had adverse health effects. After a bit of personal research, I think there's not much of an effect on health, longterm or short term, that I can see.
But yeah, I stick to what I said about not using anti-perspirant/deodorant on the hands. It's nasty. Someone will shake your hand and come to realize it's covered in a thick, sticky substance.
Stick to stuff like talcum powder. goldbond is king.
I DID see some links for hand anti-perspirant during my research, but I wouldn't look too into it. Just seems like another shady scheme to get gullible people to buy crap they don't need.