KayaJa - You may want to consider downloading Uber or Lyft to your smartphone and opening an account because of your experience with taxis. However, there are a couple downsides to consider. Available car coverage on some of the islands might be spotty and Internet connectivity may not be good enough to access the app in remote locations.
Another thing to consider... when you book an excursion through the ship, you are guaranteed that the ship will not leave without you. If you were to get stranded and miss the ship departure because of a private transportation failure, there is a very high likelihood that the ship will leave port without you. Don't believe me... check out this compilation of people being left behind - - - https://youtu.be/B-yrsXsJmbw.
The cruise ships have time windows for arriving and departing ports. Sometimes they will wait if their window allows but is it worth the risk? You have to decide for yourself.