Yorkie puppies tend to need to pee a lot. The smaller they are, the more they need to go. They also are unlikely to sleep 6 - 8 hours a night. When Max was a pup, we would go to bed around midnight and I was usually up with him at 5 am when he needed to poop. He is pad trained, which helps a lot, but he wants the poop cleaned up right away.
If your puppy only has a towel to sleep on in his crate, this is another reason he may not be sleeping well. When I first had Max, I did not know how much a dog could appreciate a nice, plush bed. (many members here would probably gasp at what I just wrote
). I brought one home and put it on the floor and Max jumped in it like he was in heaven!
What does your puppy do in the evening? If he is resting/sleeping, there is a good chance he is going to wake up very early and be ready for action. Work on tiring him out before bed time with brief play sessions throughout the evening.
I would also seriously consider using piddle pads in an xpen or a larger divided pen if you don't want to get up in the middle of the night.
Regarding the withholding of water -- despite what some trainers may say, you cannot control dog peeing by controlling water intake. Sure, I don't drink a big Starbuck's before getting into rush hour traffic on the freeway. It helps, but I still can't schedule my need to pee. Dogs don't drink just to drink. They drink only when they need it. Water is necessary for healthy kidneys, liver, heart, brain, skin -- all of the vital organs.
Dogs who eat a kibble based diet like mine do especially need water to stay adequately hydrated.