Current kit elastic shock cord (when you get elastic in a kit) is probably more synthetic than cotton.
Cotton has a higher melt/burn point than most synthetics.
Parachute shroud lines now have a higher synthetic composition.
In my Odd'l kits, I use cotton embroidery thread for shroud lines. It is much stronger than most lines in other kits. Years back, Estes and Centuri sold a stronger high content cotton Button and Rug thread for shroud lines.
Regarding the Cotton Shock Cords -
On YORF,
Bill S may have found the answer. "I've been using 1/4" SWIMSUIT ELASTIC - its cotton covered and braided. It holds up to the ejection charge just fine; I haven't had to replace one yet due to melting, unlike the less durable 1/8" synthetic covered elastic. I get it from Joanne Fabric.
I've also got a bit of 1/4" elastic that was supposed to be cotton, but turned out the seller was wrong and its synthetic. Bleh...
I'd love to have cotton covered 1/8" FLAT elastic, but haven't found any yet.
Here's a link to the 1/4" wide Cotton Elastic: CLICK HERE
There are others listed, but look for the Swimsuit Elastic to get the cotton product.