1st......If the cruise continues to offer dive excursions, the quickest access to a dive site is off the cruise. The cruise ships don’t anchor but use GPS & thrusters to maintain position in an area inside the reef, which is probably at least 30 minutes of traversing a channel to get there.
The dive taxi will take you to a dive shop on a small island. Once every once is outfitted, off to the reef.
Unless you’re willing to set up your own excursion, there’s no other way but with the ship.
I personally taken the ride into shore, but I can imagine after you did that, it would be another long ride to the dive site.
As someone else has stated, the best sites are not on the cruise excursion but that might be your only choice.