Everything
@Mitura said. Do it on your own, get there at least an hour before the cruise crowds arrive.
Get off at Havensight, find the taxi coordinators (they will have company-branded polo shirts and lanyards), tell them you need to get to Red Hook.
At Red Hook, buy ferry tickets to St. John (buy the round-trip tickets, and save a little time and money on the trip back). As you get off the ferry in Cruz Bay on St. John, you will see a ton of taxis, vans and jitneys waiting for fares. Tell whichever driver you’re directed to that you want to go to Trunk.
It’s part of the National Park system, and you have to pay some minimal fee to get in. Bathrooms, showers, equipment rental, limited food and drinks.
When you are done at the beach, there will be a bunch of jitneys and vans waiting for fares right at the entrance when you come out.
Just reverse your steps - Trunk to Cruz Bay. Use your return ferry ticket to get from Cruz back to Red Hook. At Red Hook, there will be people there (again, branded polo shirts and lanyards) coordinating rides back to Havensight. Will drop you off right at the little shopping area next the ship.
Four tips:
1.) The taxi fares are pretty standardized, but always ask the coordinator/driver for the fare cost before you get in the vehicle. In terms of budgeting, you can find the fares online with a few simple Google searches.
2.) The cab/van/jitney drivers are paid in cash. Last time I was there (last May), I saw a few drivers accepting payment on their phone (my guess is that they were using Venmo, Square/Cash App or Apple Pay/Cash). But that seemed to be the exception to the rule. We always bring cash.
3.) Bring cash for the ferry tickets, too. We’ve had a few trips where the computers and phone lines at the Red Hook ferry dock were down, and they couldn’t accept card payments. If worse comes to worst, there are ATMs nearby, but you might pay a hefty transaction fee to use those. I think you can now buy ferry tickets online ahead of time, but we have not tried that yet.
4.) Do not cut it too close on the trip back, timing-wise. Charlotte Amalie does have afternoon traffic, and your trip back
to Havensight could be a lot longer than your earlier trip
from Havensight. Use your best judgment, but IMO, anything after the 2:00 ferry from Cruz is asking for trouble.