I'm whole heartedly with MTS, I would simply make the binding wider on the back. Even though you haven't sewn it down not sure how putting cording in the binding would work. I would think unless you did a securing stitch that would encase the binding tightly it would simply shift inside and not stay put on the outer edge of the quilt as you envision. I'm not sure, even with the securing stitch, it would have the same look as a say a pillow with piping around the edge. A pillow is a much fatter surface for the piping/cording to nestle against as opposed to a quilt. A larger binding on the back would be the cleanest solution. I normally have it wider on the back anyway.