This is from http://www.takeourword.com/TOW113/page1.html
In England, pub frequenters had a whistle baked into the rim or handle of their ceramic cups. When they needed a refill, they used the whistle to get some service. Wet your whistle, is the phrase inspired by this practice.
Has anyone ever seen one of these mugs? A picture of one? A written description of one, perhaps? Of course not, they never existed.
Since the middle ages, whistle has been used as a slang term for the throat. As in...
Let’s have no pitty, for if you do, here’s that shall cut your whistle.
- Beaumont and Fletcher, Coxcomb , 1612
So, to wet your whistle is simply "to wet your throat".
I like the "rule of thumb" explanation on the same website:
The phrase rule of thumb is derived from an old English law which stated that you couldn't beat your wife with anything wider than your thumb.