You know what, I am not a smoker but I used to be. I actually love the smell of a cigar when I am in the proximity.
I say enjoy your cigar on your balcony!
Also - obviously, the main attraction in the Caribbean for smokers is Cuban cigars which are available on all the islands, but not on the ships (because they visit US ports). But be very careful about buying a Cuban cigar in anyplace that does not have a humidor and a big selection. Not only might they be stale as anything, they might even be fakes. Go to a reputable dealer.