Moving abroad can be stressful for many reasons. You're leaving a lot behind. Your family, friends, previous job, and a familiarity of your surroundings that makes you comfortable in life. But with the right tools and the right mindset, settling into your new life can be an incredible experience.
Before making the move, it is a good idea to do the proper research and planning. You should already have your work permit sorted, and hopefully even your accommodations taken care of. If you've already decided on your method of transportation, you're way ahead of most people. These are really the most important components of your move, so just relax and make other minor adjustments as they arise.
Luckily, moving to Cayman can be far less stressful than moving to most other nations. The weather is fantastic, people are friendly, it's generally a safe place to be, and as long as you speak fluent English, the transition should be swift. If you come from a fast paced urban environment, your most significant psychological transition may be dealing with the slower island pace, which is not a terrible problem to have.
So take a few deep breaths, and enjoy the ride. You're moving to paradise after all.