The drive to Hawk's Cay is a straight shot from any of the airports and the majority of the drive is on one road with beautiful water views.
Two possible options:
Rent a car and keep it for the duration of your trip, returning it to the airport
All the major car rental agencies have a location at the Marathon regional airport, a few miles from Hawk's Cay. You might rent a car at the airport, use it to get to your accomodation, then return it locally and catch a ride with another guest who will be driving back to the airport. Drop off fees might apply, so you'd want to look into that first.