I am assuming the Western Caribbean.
No need to take passport with you while on-shore if you have drivers license. To get back ship after visiting the port of call you need a photo id and your room key to show the local authorities. Once shown they will let you on to the pier. You then will still the room key to get back on the ship (you will also need the key to get off the ship, they use this to see if anyone is missing before they depart).
No need to get any foreign currency. All Caribbean ports merchants accept US Dollars.