Hawk's Cay is nice, the one thing is that it is a little more than a hour from Key West. Christmas week is a premium week for most places in the Keys [especially hotels] which can spike rates. Flying into Key West can cost a lot -- often as much for the commuter leg as the main leg to Miami/Ft. Lauderdale. Most people end up renting a car in Miami/Ft. Lauderdale and driving down.
If you want to be closer to Key West [19 miles] please look at
www.waterfrontkeys.com for Venture Out. Mixture of newer manufactured homes and older mobile homes with a variety of prices. Most are waterfront where your boat would be 10 feet out your back door. Has pool, tennis courts, small store [with gas], etc., in a gated community. Great access to both ocean and bay so you can do a range of fishing and snorkeling/diving.
December is a toss-up month for weather -- because of wind. Water temperatures normally in mid-to-upper 70's, air usually upper 70's, but both can change quickly [both directions] based on cold fronts.
If you have any questions, let me know.
CudjoeDon