Do you have a Northern or Indonesian BTS?
Mine pees a lot too. Normal, odorless, and urite comes out at the same time. Cocofiber does a great job soaking that pee up to help with cleaning. A nervous BTS will defecate/pee if they don't want to be handled.
However, once the skink did his business, you can take him out and he should not go potty again. They usually will go once a day so you don't have to worry about it after he had done it.