Well, yeah.
But then you have the old "standard" HV cable already laid out from end to end, with a good place on shore for tooling. You then use the old HV cable to pull the new water-rated cable back out the island. /sarcasm
( By the way 1, find out if the installation is near the ocean shore, or across salt water with tides, high winds and storms possible (???) or across a simple fresh water lake with static water (????) or across a river with widely varying currents and flows?
( By the way 2: To get an estimate, CALL PEOPLE in the industry.
"Hi (fill in name of cable company provider), you don't know me, but I'm setting up a bid for a high volt, 4000 foot submerged cable approximately 4 feet in depth from shore to an island. I'd like to talk with a sales representative about potential ways of doing this, and to get any recommendations your engineering and specifications staff can provide about this kind of cable. "