The same day I organized my ribbon, I also went through my stash of cord. My chimney hats, for example, use cord for the "tails." In the past, I have simply wound cord around a piece of cardboard and kept them stashed together in a drawer. This method is easy to view but will bend or mar the cord over time, causing wrinkles and ridges and necessitating ironing before use.
Now I use pieces of clear flexible tubing (acquired at any hardware store) to wind my cord on. Be sure not to use tubing that is too thick or it will be difficult to cut. If you cut a small wedge into the end of the tube, you can use that to catch the end of the cord so it doesn't unwind. Otherwise, fastening with a safety pin works.
Since I use cord infrequently and don't need to see it when designing something, I can keep this thrown into a drawer instead of on a rack. (Note: flexible tubing doesn't roll on a dowel very easily. PVC pipe does.) Of course, you can use anything else that is tubular for cord, just remember that ribbon is flat and doesn't create much bulk when wound, whereas cord is bulky.
If you want to see your cord while working, you can stick your tubes on a spool holder like this one.
I just keep mine in a drawer.
Final hint: Toss those small end pieces of cord (less than 1/2 yd) into a plastic zip-bag labeled End Pieces and keep them in the same drawer. Now go to town & untangle your stash.