Depends when you leave for your excursion. We had an 8 am Nassau day (shops and Market don't really open till 8:30-9, on a weekday, don't know about weekend) but we had a 10:45 excursion. We got off the ship at 8:15 went to Starbucks (they are open early) and walked around. Shops started to open, then shopped till about 10 and were back at our excursion meeting place on ship at 10:30. I noticed the Straw Market was open on the way back but didn't stop in as we had to get back. There weren't a lot of people there yet and was way calmer then when we came back from excursion. Seemed crazy when we came back from excursion.
Edited to add, The Morning was a great time to shop no crowds at all and we were in and out of each store we planned to go to quickly. It was much more enjoyable then in the afternoon, albeit we had to wait a little for 2 to open for us.