Good call.
A trick I've used when threading cords through hems is to use a piece of music wire, available at any hobby shop, and to rough one end up with a file and roll over the opposite end. The rolled end pushes easy through hems and prevent stabbing yourself if you have to force it.
I attach it to the cord by gooping it with superglue and jabbing it down the center-line from the cut end. The excess squeezed out is used to form the end so it tapers. Liquid superglue works best for the first part and gel for the second. In a pinch I have used electrical tape to form the taper.
The piece of wire can then be threaded anywhere you need it. Once through you cut off the glue soaked cord. The wire can be reused by scraping it with a knife.