Go to a local sign shop and tell them the same story....
The rolled vinyl that is used for truck lettering, banners and signs is actually a giant adhesive sticker and comes on the backing...usually from a 36 inch roll....so any banner shop will be crumpling large sheets of these into balls daily.
Static clings come the same way at a sign shop...on roll on backing. If you stop in and ask them for a sheet of it from their next project, they could roll it up and rubber band it for you. Look in your town for a sign-o-rama or fast signs...a large franchise does so much work every day they may be able to provide you with some on the spot. If not...ask them and tell them you could stop back in a couple hours.
If that's not a possibility....I'd say lay them between two bed sheets....roll it around a wrapping paper tube and slide it into a fed ex mailer....any lint can be washed off of the vinyl at the new house and laid out to dry. If they are small....scotch tape them to the side of the washer or refrigerator...they will dry and flatten at the same time.
I never used wax paper, too concerned about the film it will leave if it gets warm.
*****After reading responses
YES THEY WILL UNCURL!!! LAY THEM ON A FLAT SURFACE
All static clings are from a roll, and then fed through a printer then cut.....they uncurled once, they'll do it again. If it has the light adhesive...it should also we washable. It regains stickiness once its dry...do not leave soap on it or use any type of alcohol or ammonia base on it.
FYI...long term, roll them with the print on the outside. Long explaination as to why, but seriously, it's true.
The key is not to crease or try to heat it up to reshape it. very very low heat if any. The vinyl was formed in a shape and will naturally want to return to that shape it was in unless its stretched, heated or creased. If you use wax paper....use a harder cardboard to put them all between, you do not want something leaving a divet or crease in them.