Straw Market: Yes they have one...
The straw market here on Coco Cay is even more disappointing than the others around the Caribbean. I personally only saw 1 item I'd consider and I didn't consider it long.
Save your shopping money for other places and just relax and have fun here.
Shopping can be had elsewhere.
There are lots of little huts with shops which sell screenprinted t-shirts and sarongs...they're all overpriced, I wouldn't recommend it.
What to pay: Too Much