The wider grosgrain I find helpful for shoulder straps, for simply strapping the drybag to the packframe, lashing would be the lightest. For convenience sake, Roger's right, thin nylon, or I would suggest, even the grosgrain ribbon might work, though it doesn't hold as well in the ladder-lock clips.
Definitely get a quality, lightweight webbing, but be wary of anything labeled "robust." If you're ordering online, which is usually the best way to get exactly what you want, it's usually best, and not ultimately that expensive to have them send you a sample pack. Quest, OWF, Thru-hiker, Seattle Fabrics will all do this for a small fee.