Well, it depends on what kinda nut you have. Locking nuts are the easiest, because they usually unscrew at the back of the neck and you can get a piece of card or metal to stick under it and screw it back down.
If you shim the neck, it sounds to me like you'd wanna shim the front of it--i.e., the part that is farthest from the guitar body. Neck shimming is mostly trial and error as far as finding the right height and so on goes. Most people use business cards or even playing cards to shim necks.
Sticky thing? Got me.