You would have to take a cruise ship. Plus they take days to get somewhere and it is a waste of your vacation.
Planes are not that bad in fact i actually like them, and i am terrified of heights as well. But you see once you have ascended and the plane is flying normally, it doesnt even feel like your flying and you will soon forget your even on a plane, except when you have turbulence and its actually pretty fun, except for all the cramping and boredom, but you can always take your laptop/ipod/phone and entertain yourself, or just sleep through the trip, the worse part are the back pains and cramps from sitting too long, but you can always stand up and stretch or go to the bathroom, i would reccommend eating in the airport for the snacks are very light and some airplanes dont even provide snacks. And try not to travel in a messy stomach, for things can get ugly. But most importantly relax and close your eyes and it will feel as if your on a rollercoaster, i actually happen to LOVE planes and i am terrified of heights but there is no need to look down, just look straight to the side, or after 45 minutes you can look down and you'd probably be over the ocean by that time depending where you departed from.
Then again try going to phsychology or google how to get rid of height phobias. It worked for me (i used to have a horrible fear of heights).
So just try it, i promise its not that bad. Bon Vojage =)