If you opt for a place like Salt Cay you will want to check if there is anything open during that time. We went to Middle and North Caicos last August, which was a very interesting experience. But, because it was hurricane season, a couple of the little restaurants were boarded up and closed for the season.
If I recall correctly, the diving in Salt Cay is much different than Grand Turk - not so much of a wall, but more likely encounters with some big life - like sharks.
Many years ago we did a 1 week liveaboard out of Provo (did Provo, West, French, Salt) and then did a week on Grand Turk. The diving in Grand Turk was a bit of a let down after the liveaboard. We got spoiled...sharks, sharks, and more sharks, turtles, eagle rays, and dolphins. It comes down to a matter of preference and comfort.