1.) Systemic antibiotics (!!!!!!) ASAP.
2.) Supportive care; heat, food, water with pedialyte or vitamins, confine to quiet area where she can heal.
3.) No safe way to sedate without veterinary-quality drugs, I wouldn't do it. Any type of anesthesia depresses the whole system- heart rate, breathing, etc., and without proper dosage/monitoring (i.e. gas anesthesia machine or well-measured injectable drugs) it will probably do more harm than good.
4.) How is the skin flap? does it look "alive" with a blood supply going to it, or does it look like "dead skin" dry, darkening, etc. If dead/dying skin, then it would not re-attach anyway.
5.) I know this would be hard 'cause it's her NECK, but can you gently clean the area and then try to wrap it a bit? If you can keep any viable skin against her neck for a couple days, it will probably re-attach without sutures.
Edited to add: okay, this idea may be a bit goofy or not work, but would a sock or stocking with a hole cut out at the "toe" work as a makeshift bandage to keep skin in place???? I would clean it, apply triple antibiotic ointment (to help prevent infection AND to keep it from sticking to bandage and re-ripping), cover with gauze padding, then try to put sock over her head around her neck to try to keep it stable... ???????????????????????????????????????