Having had the same problem on installing a number of replacement
glass panels that I have manufactured over the years, I offer the
following solution.

Get regular cotton, not a synthetic, clothes line, or sash cord,
and dye it with "Rit" fabric dye.  Just make it as concentrated as
possible and leave it to soak for the maximum, according to the
directions on the box.  It looks as good as the original, because
that is probably what they used.

Walter Kehoe
Syosset, New York, & New Port Richey, Florida