The rules have changed for scissors as noted above. But be aware that if you are traveling outside the US, rules may differ. My cute thread snips were confiscated leaving Turks & Caicos last summer. Nothing was posted in the check-in area to warn of that or I would have transferred them to my checked bag before going through security. I've also had a pair of child's safety scissors taken in Japan. Short blade/rounded tip scissors have been allowed on board flights for the past decade or so (I talked to multiple TSA screeners during that time and generally put the scissors in the same bin with my shoes so that they could see them easily.
TSA used to forbid the cutter style necklace because of the hidden blade. It is not expressly forbidden on their list now. People have used dental floss containers in the past as a cutter as well on planes.
Cheers, K