Things I did in the past month that I would have been really scared to do 15 years ago:
* get a pedicure and a massage!
* attend a business event, introduce myself to people and initiate a handshake!
* go shopping for an engagement ring!
* sign up for a retreat with huggy people who like to do crazy things such holding hands in a circle!
I'm becoming a big proponent of the "full disclosure" policy for those situations when someone will need to touch my sweaty hands or feet for an extended period of time. I say something like "You might notice that my hands (or feet) are really sweaty. It's because of a medical condition I have, not because I'm nervous. My sweat glands seem to have their own schedule, and they won’t tell me what it is." When I communicated this to the massage therapist, she said "thank you for telling me." Ironically, I end up sweating less because I feel less nervous.
I don't recommend full disclosure for more formal situations such as business meetings, but in informal or spiritual settings, it works great. Don’t apologize, just state it in a matter-of-fact way. Don’t deprive yourself of the connections with others that you need and deserve.