Caymanian Citizenship is out of the question. Forget about it. You also definitely will not be hired to guide dives.
As for the rest, I don't see things as being so bleak.
There are tons of jobs in Cayman that require little or no formal qualifications. Yes, there is a Caymanians-first requirement, but many service sector (and other lower paying) jobs do not attract a sufficient number of Caymanian applicants.
You could apply for any of a number of jobs working on snorkel boats. There are jobs as boat crew and positions are available shooting video (though some operations may require at least AOW for shooting video) with many operators. Many of these are doing trips to Stingray City - posible 2 or 3 times per day.
Other companies hire beach attendants. These positions do not require much specialized skill, and some of these companies also have dive operations. That may come with free diving (and maybe even some additional instruction) on your day(s) off. Check out Red Sail Sports, one of the largest watersports companies in Cayman.
Most employers want at least a 6 month commitment. This is the length of the most common temporary work permit. The employer must pay the full cost of the work permit (it's the law), though you may bear the costs of the medical exam and such required for the application.