About this second part of your question, "Should you book prior, or wait" let me offer what little I can. FWIW As you can tell from my previous post, I tend to be very cautious when I plan things, so we don't often book on our own. I like knowing I have reserved what I want (IF I have something specific in mind.)
But that being said, all three of your ports are places where finding excursions on your own should be fairly easy either booking on line or at the pier. (And fairly safe. You can't say that for all ports.) Just remember, that booking at the pier will use up some of your limited island time, and may not be as easy to find exactly what you're hoping for.
As to being the only people on that 3rd party excursion, I'd bet the answer is likely not, unless you specifically book a "private" tour, designated as private or "small group" when you book. There are some to be found. The ones that take just your group of four, six or eight, on a sailing ship really look like fun and often include lunch along with the drinks. I've always wanted to do one, but the few times we've cruised with a small group, finances were a concern for some and those "private" sailings were too expensive.
We have, on occasion, booked an excursion independently and found we were on the same excursion as other cruise ship passengers. So you may get precisely the same excursion (often for less money.)
What you don't get with any third party excursion is the assurance that you will get back to the ship in time for sail away. So be very specific about timing when you book. And try to book your independent excursion for early in the day, to give your self a little time cushion should you return later than expected.
Even after 21 cruises, we still book most of our excursions with the ship, and consider the difference in price as a mini- insurance policy. (If the cruise's own excursion is late getting back to the ship, they will either wait for you, or it's their job to catch you up with your ship)
Lastly, as to whether a particular excursion is fun or not, really depends on the people. We've always enjoyed our excursions (whether book with the ship or elsewhere), some have been merely pleasant, other were a blast. Seems to me that if you are going with those friends that you mentioned, you'll have fun no matter how you book.
