My friend has the very same problem; his hands are always sweaty and he tells me it gets worse when he shakes peoples hands.Sometimes his hands are dry but then something about feeling self-conscious that his hands are going to sweat when he is going to shake someone's hand or hold someone's hand makes his sweating worse.This condition is called hyperhydrosis (people can have it on their hands and feet, and/or the armpit area) and it is bothersome.I don't know of a good product that you can buy that will offer dry palms, but maybe surgical treatment can be right for you.Here's a website where you can learn more about this procedure:
http://www.handsweat.com/hope this helps!