It's extremely rare for anybody to get a job in Cayman from abroad. The most that might happen is that you will be offered an on-island interview, but usually you would have to pay for your own airfare - and maybe get the money back if you get the job.
Cayman is a very enviable place to live, and every man and his dog wants to find work here. Good luck to you all, but without some kind of personal contact here, your hopes will most likely come to naught. I'm sorry to be the bearer of bad news.
