The drinking water made me think of this: when I first started giving presentations (I present and give workshops at teachers' conferences as well as teach), I would be so nervous (without it showing) that I would be shaky. When I picked up a glass to get water, it was really obvious.
I find that a better way to deal with dry mouth is to drink some beforehand (NOT cold water, as this can make your bladder feel like you ave to pee! room temp or even a bit warm water), and use toothpaste, rinse and/or gel made specifically for dry mouth. (I don't get nervous now, so I don't need those tricks anymore!)
Also, "thinking at your audience "I love you (or I like you, if "love" makes you feel uncomfortable) and I want to share with you" or something similar, can help put you in a frame of mind to be more relaxed with your audience.
Another technique I've heard of for relaxation: as you practice relaxation, associate a relaxed state with some easy-to-use physical signal, like touching your thumb and middle finger together. Once you practice this for a while (maybe not in time for the upcoming speech, but more a long-term tactic), you can program your brain to react to the signal and relax automatically.