The schedule that cj22carcar left looks good because with a formal day on Grand Cayman, you won't have any problems. I know that when we were there on Princess, we left port at about 3:00.
The problem (not a problem for us) with 5 port, 7 day cruises (we are taking one in April), is that there is only 1 day at sea, so there will be a formal night on a port day. :0)
Star Princess - December 2006
Adventure of the Seas - April 2005
Caribbean Princess - July 2004
Golden Princess - March 2003
Disney Magic - October 1998