jenny, there is a glue called Shoegoo. It's transparent and comes in a tube, and it sticks almost anything. Has to be used sparingly for a handbag job, but I would suggest it would work well if you unravelled the gold strap a few turns and then applied Shoegoo to the strap and then re-rolled the gold strip and held it in place with maybe a clothes peg for 24 hours. When it's dry you won't notice the glue. It's designed to hold shoes together and is good and strong, but flexible. Might be worth a try.