The biggest chance you take on a cruise is falling down and hurting your self, going off your diet, or forgetting your meds, certainly not being attacked by the natives.St Thomas you should feel safe and secure, also the Bahamas, where the ship docks.
St Thomas maybe, since it’s a US Territory but anywhere that the US Constitution isn’t in effect will be a hard “NO”. I’m sure it’s fine but I don’t take chances if I do t have to.