If the diver is able to reach the edge of the island, are they then allowed to swim around the edge to reach another tile on the edge of the island?
Logically this would be sea, just as removed tiles are, but I suspect that this is not allowed.
In addition to being able to move normally, the Diver may move through one or more adjacent missing and/or flooded tiles for 1 action. A missing tile is one that has sunk. This has been confirmed by the game's creator.
I suspect you're asking if the board "wraps around", can the diver swim from the left side to the right side? From the top to the bottom? Answer is definitely "no" on that one, it would be mentioned in the rules if it was.
As to the other possible question you might be asking, "can the diver swim through ocean to get to another island tile", there's no need. The island is square-ish so you can always traverse from A to B by staying on the island.
Perhaps you're wondering if the ocean can be used as a short-cut somehow? I really don't see how. A square is still a square. You need to be the Pilot in order to move more than 1 square at a time.