I am sorry you will miss the brewery. It is our first stop when we go to Grand Cayman. The duty free shop just outside the port (the small one with the indian outside - not the main one you can access from inside the port) sells Caybrew. I think the main duty free sells it too - but I have only purchased liquor from that store so I can't be 100% positive. I haven't bought from them lately as we buy it at the brewery to know what they carry, but they did carry several of their beers. Last time we were there they did not have things like Mango Tango which is my favorite, but they did have Ironhorse, 345 stout and the main stay Caybrew Lagers. There is a bar if you turn right outside the port that serves their beers on tap - but be prepared, it will cost you a pretty penny = If memory serve me correctly it was $25 US for 2 pints and a tip.
And if you like craft beer, when you go to Cozumel walk down to Mega. They have a unique selection of Russian, eastern European beers in bottles. Just be careful - last time we were there they wouldn't let us buy beer until after 10 or 10:30. We ended up wandering around the store for 45 minutes waiting to pay. That was new this year.