Surely you don't have to hoard your cord! There must be other suppliers of the same or similar product! Some cards just look so good with this cording on it.
I find that you could just make a tiny little nick with you sharp scissors at the top of the paper exactly where you want the cord to go it will stay in that little cut. then flip it over and tack it with a glue dot or ATG glue. If you punch out an ornament shape then hide the cord under that..
then attach your corded card on top of the main part of the card with glue and it should stay!
I find that if you can find another source of the gold or silver cording.... the elastic kind is easier to tie.