I drew it up as a cinch, but of course it wouldn't scrunch up at all, but create more of a fold than anything (unless you enclosed the shock cord in a sheath anyway, negating much benefit over a drawcord).
Maybe what Dale was talking about in the first place wasn't what I drew, but rather small loops positioned a couple inches from a button to simply "take up" a portion of the hem. This would also create a folding/protruding effect on the hem, but would be easy, light, and quick to do/undo.
The grosgrain would be easier to work with to get an even, nicely sewn channel, but a strip or tube of fabric could be used too, at some cost to durability-the benefit being that fabric might scrunch more evenly and easily than a full circumference of grosgrain. Even so, if the OP is looking for ease of installation, the grosgrain seems like a really good idea. Just cut to lenght, sear the ends, and install.