It's been a while since I've flown. It used to be you could pack a change of clothes and all your cosmetics (Razor, Mustached scissors, Fingernail clippers, shave cream, etc) on a carry-on so you can make sure that stuff is available if luggage is lost. Are you still allowed to carry the cosmetics on board? Or are you made to check it in with the rest of your luggage.
Rather than guess go to the source of the rules. A visit to the Transportation Security Administration web site (www.tsa.gov) will provide a list of prohibited items that you can download or read online.
Crown Princess March 2017
Explorer of the Seas October 2013
Caribbean Princess July 2006, May 2010 & November 2012
Monarch of the Seas November 2008
Crown Princess November 2007
Celebrity Zenith November 2005
Enchantment of the Seas August 2004
The rules have changed (and since the original rules, have consistently become less stringent) so things that were prohibited just a few months ago may not be prohibited a few months from now. (Of course, things could end up going in the other direction...)
I would guess the scissors would show up on the machine, then they would have to take them out and check them -- if it were me i would leave all the metal stuff in my checked bag to avoid them having to look through my stuff. Even if they say they are ok because of the rounded edges, I would just rather them not open my cosmetic bag.
As mentioned the rules seem to change and from airport to airport, TSA follow them as they are instructed. Put all nail implements in your checked luggage. We were behind a young teenager at security before flying to our last cruise and they checked her "bag" over and over again before anyone else could go through. She had just received one of the Clingque Nail kits as a gift with purchase and had it in her backpack. The implements were no more than 3 inches large, but she had to give it up or go get her checked luggage back and put it in there. My DH and I both pack our bathroom bags into our small roll-on cases and check them with the big luggage. When we get to the airport, we just keep the smaller suit cases and roll them onto the ship. We don't worry about not having the "change of clothes" either. Always pack your jewelry, medications and of course travel documents in your carry on.