You will need to collect your baggage to go through Customs so you should have access to stash your duty-free liquor in your bags before you recheck them for the flight to Brac.
I recently read that the airport now has an indoor corridor connecting the arrival lounge and the ticketing hall. That's nice because last month we needed to maneuver a broken luggage cart (that tipped over!) around the traffic and construction outside in order to access the ticketing hall to check in for our next flight.
But I haven't heard anything suggesting that the in-transit process has changed; so it is likely that you will still have to collect luggage, go to the ticketing hall to check in with Cayman Airways, recheck your baggage, and then go through Security to access the departure lounge and board your flight to Brac. And of course you cannot take a bottle through Security so you will need to put it inside your luggage before rechecking.
How much time do you have at GCM between flights. If you have a bit of time, after your check-in for Brac and recheck your bags, walk outside the ticketing hall and look for a sign advertising the free shuttle to the George Town Yacht Club just a few minutes away. The gray van for the GTYC make regular trips to and from the airport and you can also call the number on the sign and ask for a pick-up. If you have some carry-on bags they will stash them for you at the restaurant.
GTYC is a lovely location (both for indoor and outdoor eating) and they serve breakfast early on Saturday and Sunday. Their lunch menu is also great and we love their Cracked Conch. So if you have the time it is much nicer than waiting around the airport:
George Town Yacht Club
I will be interested to hear your report about the current status of the airport construction and the process for inter-island travel. When we were there the departure hall still wasn't completed, and that may still be the case. There were few amenities or vendors, tiny washrooms with long lines, a poor sound system, and not enough seating. But it was still under construction so it's got to get better soon!
I was happy to see that many of the other GCM processes were much improved during our recent visit, especially arrival, immigration and customs, and security.