I've never felt the need, but this is how I would go about it. Open the blind all the way to expose as much cord as you can. Place a step ladder next to the window. Mix up some oxyclean and hot water in a quart bowl, place the bowl on the ladder and drop the dirty part of the cord into the water and let it soak for maybe 30 minutes. Rinse using a separate bowl in the same manner. Pat it dry with a cloth, let it hang down until it dries, then close the blind.

Or, you might try running a Mr. Clean Magic Eraser along it.

Thank you, graywings. I'll try Mr. Clean, the other method sounds a tad tedious!

Pull the shade closed, loosely wind the dirty cord around your hand, slip your hand out, spray the dirty cord with diluted degreaser, dish soap etc., roll the now soapy cord around between your palms and then slosh it in a bowl of water or use a wet towel rag to rinse it off. DO NOT get the degreaser or any concentrated cleaning spray on the blind or shades themselves. Don't use any strong cleaners on dark colored cords unless you didn't like them dark.