I would probably do something like this: And depending on how big you make the gaps, there wouldn't even be a need for an alpha-map to mask it out. And if you really want some volume in there, then the same thing with a shell modifier could do.
Make a cylinder which follows the shape of the cord and bake the high poly onto it. Remember to place a cylinder in the middle of the cord of the highpoly to compensate the gaps, so the renderer doesn't read through the gaps. Use a alphamask to mask out the gaps, like Adam said. I used the same technique for the cord on my…