What Are the Laws on Grand Cayman Island?

http://www.rcips.ky/files/firearms_apps_form_a.pdf.

Here is a link. Google is your friend

Phriend: THR is also your friend. Does everything at that link make sense to you?

Unless you own a significant amount of property and have a significant bank account and can prove you can support yourself, you aren't moving there. Private firearms ownbership is not permitted.

Add to that it is one of the most expensive islands to live on in the area.