Assuming you have typical, small manicure scissors, you should have no trouble bringing them onto the ship. Tweezers, nail clippers, and nail files are fine too.
For luggage that's going onto the ship, the same security restrictions apply to carry-on and checked bags. After all, both wind up in your stateroom, and you have access to everything in them. Pocket knives are prohibited, but small grooming tools are fine.
Regarding scissors when flying, the TSA allows plastic or metal scissors with blunt ends in your carry-on bags. However, if you have scissors with pointed ends, they must go into your checked luggage. Tweezers, nail clippers, and nail files are allowed in carry-on and checked bags.