I don't think you can from Key West they normally take it at the ck point and give it back to you at the end of your cruise. If you could there is several places right when you get off the ship after you get off the trolley.
On the Eastern itinerary we have always been able to keep our booze bought in port with us. We always pick up an additional bottle of Bacardi for onboard consumption.
If you purchase anything onboard, they will pack it and hold it for you until the last day of the cruise.
Not sure if the same holds true for the Western.....