I bring that kind of stuff all the time. I always have open bags of snacks in my book bag that I acquired on my journey to the port. Once it is 0n board though it can’t leave the ship.
Solo studio is smaller and the bathroom is configured completely differently. Solo inside is a regular inside cabin, with a regular bathroom and about 35% more space.
You haven’t looked very well if you have never seen anything electrical in an NCL bathroom. I have never sailed on an NCL ship,that does not have an electrical outlet for shavers in the bathroom.