Shore options v set excursions East Caribbean

I am looking for recommendations for doing set shore excursions v finding our own way of getting to a beach, relaxing, snorkeling, having lunch, et al. We love great, calm, white sand beaches but don't really enjoy 'relaxing' with hundreds of others while be herded from one place to the next (yes, i know that is what cruising can be like!)
Are there options to find a day sail/snorkel or someway to get to a great beach with chairs rented or provided and picked back up & taken to the ship? Or are those things just not reliable, safe or cost effective?
Islands we will be stopping: Tortola, St Kitt's, Antigua
Thanks!

I agree

While on the ship, get a list of shore excursions and see what interests you. When you go ashore, you can book directly at a great savings. Only problem might be, that if you set it up yourself, and something breaks down, or you get detained for whatever reason, the ship will not wait for you.
If you book on the ship, then you will pay more, but the ship will wait for your tour to return if anything happens.
The tours that the ship uses are usually the better operators, where if you book it yourself, you are at risk of possibly not getting what you expected.

Just my opinion, but I think that the private excursions are just as good - although in any specific case can be better - can be worse. Also, the reputable private operators will do whatever is necessary to make sure their customers will make the ship - they will call in other operators and get help if something happens. Is it possible to miss ship - yes, it is possible - but an extremely extremely rare event.

Agreed. We have booked many excursions on board, and also just went ashore and booked them with a private operator. We have never had any problems in either situation. Just a possibility something can go wrong no matter where or what you book, and if "Murphy's Law" kicks in, you would be in a better situation with an excursion that was booked on the ship. Just trying to help.

If you want to set up day sails, you should do your research and book on your own ahead of time. If you want to take a tour, you can generally get off the ship and do it on the spot. Most ports have a "preferred provider" of shore transportation, a taxi union that is allowed to pick people up off the pier. To get a better deal, you may have to walk a bit. At Antigua, you will run a gauntlet of taxis in order to get to the "independent operators". Again, find out what the taxi license plate looks like in each port. There are people who "gypsy cab" illegally and there are people who drive minivan buses that will charge a tourist taxi fare. If you know where you want to go, tell them, otherwise you will be taken to a tourist beach. Let the buyer beware!

I've done it both ways, on over 50 cruises.
Depends on the ship size, passengers, destinations etc.

With The Internet of Things, very easy with just a little bit more effort, very well worth it to plan your own. Learn to research and negotiate. Enjoy the lack of crowds and waiting on stragglers.