I have seen eyeglass "bands" (I actualy owned one at a time) which were made by taking a flat narrow rectangular pcs or neoprene ( the stuff wetsuits are made of) and just sewing the sides of each end together about one inch long making an sleeve open at both ends. Since the material was somewhat elastic you just slid the watchamacallit into the sleeve.
Other eyeglass cords I have seen all had a loop at each end and a little plastic or metal ring that you would slide up the loop to secure your whatchamacallit in. I guess you could just loop your cord, sew it that way and then use a pcs or silicon tubing to lock the wa.... in .
you can get the tubing at the hardware store or even at a plumbing supply, or aquarium store. loop your cord before hand to measure the thickness or the whole thing this will be the inside diameter of the tubing you want.
most store sell this stuff by lenght ( don't let someone sell your a roll) you can most likely by just what you need ( an inch or so) for 0.05$ at worse you will need to buy a foot ( 0.60$)
good luck
Jean ( the 401 hater)