Everything on the ship is billed to your own board account. Cash is not allowed/accepted. You register your credit card early in cruise and get the invoice on the last night. If OK (it will always be MUCH MORE than you expect due to compulsory gratuities etc.) do nothing and you get final PAID confirmation.
So cash is only needed for ashore. Expensive souvenir shops will accept c/cards so you just need enough cash for "holiday" purchases. Assuming you are on a big US ship calling at all the usual islands (some with their own currency) they all have accept USD as 99% of the visitors are US.
So leave "bulk" dollars in your cabin safe and take c/card and - say - $100 for drinks etc. Assuming you have taken a ships excursion the cost is billed to your ships account, you just need cash for drivers/guides.
Spread the money ( and therefore risk of loss) between you. For women it is safer to have money belt, do not have any valuables in a handbag! NEVER use/take an expensive looking handbag!