Your ship calls at Philipsburg cruise port. A private boat takes you to Anguilla in about 30 min and brings you back with margin on the all-aboard time — not on a tour operator's schedule.
Shore excursions leave in groups and come back late; the public ferry does not wait for a cruise passenger, and missing the all-aboard at Sint Maarten means catching up with the ship at your own cost.
A private boat departs on your time, covers the 23 km in about 30 min, and the return is planned backwards from your all-aboard.