Yes, once you reach the story part were TC (the stewardess) shows you where the Restrooms are, you can go there to delete the Pee Gauge and Clean yourself. It's at the right hand from the Mofu Kingdom's Gates.
Story Mode Nishy is indeed in a constant Shy state, which will be reduced according to the Story Progression.) Remember to always use a Shirt and Pants. You can avoid this by drinking your fapets milk once you pass the Bar First Impression story arch.
Free Mode Nishy doesn't have that limitation tho.
If you feel the game slow, I'll suggest you to use a Speed Hack, preferably the once included within Cheat Engine.