THe post office operates on ONLY cash, not KTTW charge. Post cards were 65 cents. They use BAHAMIAN stamps, so you can't bring from the US. Bring change or dollar bills--they often won't have change for you, especially early in the day. People who have nothing smaller than a $20 bill are out of luck!
You do have another option. You can pay GS for the stamps to have the postcards mailed for you. There are times that the post office doesn't open, or doesn't open on time (the post mistress has to come by small boat from another island). If this happens, GS will get your cards mailed from CC on the next cruise. Even if the PO does open, this approach saves you stopping at the PO, worrying about change, etc. You can handle it all before your Castaway day unless you want the thrill of standing in the Post Office line on Castaway.
And...if anyone cares...post cards from Grand Cayman are 25 cents US and they are not allowed to give change in US money. So you either have the right change or will get back Cayman Dollars.