Do you mean that you want to be at the beach until 4?
If I were you I'd start driving around and becoming familiar with Nantucket. Stop for breakfast and for lunch. Maybe use this time for your visit to the Whaling Museum and lastly hit the grocery (an/or liquor) store for supplies.
When I was renting our house a few regulars knew they could call me to see if they could get in early. If you are not renting direct then plan to call the realtor who may agree to take the time to check as to whether the cleaners have completed the house or not. Usually the realtor has a key staff member who arranges and oversees the cleaning. Talk to that person if possible.
After all, while some houses are cleaned at the end of the turn over time, others are cleaned at the start. Maybe call and chat with them now or any weekday just never call on a summer Saturday unless urgent.
Enjoy your holiday Amanda.