Hi LI_Pets and welcome to cruise-chat.com.
My general rule for booking ship excursions vs. going on our own is that the further the site is from the ship, the more likely I am to book through the cruise line. This is precisely for the reasons Bob E stated in his above post.
For instance, we once had a tour in Norway that took us well inland into small towns. On the way back, our bus broke down. As we were on a ship excursion, our location and predicament were known to the ship staff, and another bus came to retrieve us about an hour later. I have no idea what we would have done if we were on our own. We would have been at the mercy of the tour organizers, with no guarantees.
On your itinerary, Nassau is pretty easily done on your own, as Penny stated. Great Stirrup Cay is NCL's private island, so the only excursions you'll find are through the line. Of course, you can still snorkel on your own if you have your own gear.