I had a cut on my hand that I was putting tea tree oil on. I noticed however after 2-3 days that the really bad sweating on my hands had stopped!
I added 6 or so drops of tea tree oil to around 3T of olive oil and covered my hands in it before I went to sleep. The tea tree oil meant it was absorbed quickly, but you may want to alter the timing if you are concerned about the oil getting onto your sheets.
I did this for 2 nights then stopped and it was almost 2 weeks before I noticed the sweating was becoming a problem again. It didn't completely stop my palms from sweating but now I don't have to be nervous when I go to shake hands etc.
*the season has also just changed (spring>summer) so I don't know whether that also had some effect.