Smugglers Cove will certainly be the "road less travelled" in terms of cruise passengers. Taxi there will be no problem, get in any cab, say "smugglers cove" and off you go. Problem may be in getting a cab back. You can make an arrangement to get picked up by the driver that brought you, but, if he gets 8 passengers at Cane Garden Bay you may be walking a long way back to Road Town. When are you going? Smugglers Cove can be awfully quiet in the next few months. Not a lot of cabs hanging out waiting for fares.
Many hotels and restaurants close in September and October in the BVI's.
This is the slow period, hurricane season and for those in the hospitality business their opportunity to take some time off. Smugglers is not the "main" destination of most cruise passengers. It probably isn't even number two or three. Your best bet is to make a round trip arrangement with a cab driver (and withhold some or all the money until the return). Regardless give yourself some extra time to get back to Roadtown. Unlike Cane Garden Bay, the cabs will not be lined up to take you back to the other side of the island at Smugglers.