Any Hotel Beach is likely to be fairly busy during the holiday week - Secret Harbor is no exception and not too big a beach to start. You could try Lindqvist Beach/Smith Bay Park which is much less visited than most others -- You could rent a 4 wheel vehicle and drive down to Neltjberg Beach and probably see no one else or park it and hike down to Stumpy Bay -- Brewers Bay Beach, past the airport doesn't attract much cruise ship traffic and is spacious with calm water -- Hull Bay usually has plenty of open shaded spots to enjoy and good snorkeling if the seas are down - a day charter on a power boat would give you access to quite a few deserted places - Hiking down and to Mermaids Chair [ and back up] is spectacular and rarely visited and accessable from the gated entrance to Botany Bay Estates -- Platform Beach or Little Magens on Peterborg peninsula usually have few if any beachgoers - Lots of options to "avoid all the people".

Mermaid's Chair is quite the hike back up so unless in good phyical condition, you'll be struggling.
Just be aware that it is not always safe to go off the beaten path by yourselves to isolated spots so don't take any valuables, if you do, that cannot be easily replaced.

Winter is our high season so most of the popular beaches will be full of all you snowbirds
enjoying our beautiful weather, waters and beaches.

If you really want deserted beaches, come visit us in Sept.

Coki Beach can be quite the zoo with any cruise ship in.

Secret Harbor & Coki will be busy with cruise ship people.

Best bet is Smith Bay Park (Lindquist Beach). There are no facilities, so bring your own food & drink.

They do have picnic tables and porta potties/Smith Bay Beach. (a/k/a Lindquist)