The common currency is the US$ so no need to take a range of currencies you cn also use your credit cards. If there was one island that was a problem you could get the local currency on the ship albeit the exchange rate won't be so good, but I think this unlikely.
You will be able to use US$ on all islands. It is worth noting that the french island of Martinique uses the Euro, but will accept $$ and will give change in euros.
The American Dollar is widely accepted in the caribbean, some islands do have their own currency but they still accept the dollar i came back from a caribbean cruise last sunday. michelle.