Normally the game does not allow you to access Diamond Steppe Island until you have the hookshot. However using some clever tricks, it is possible to get inside the island early. Obtaining the Ghost Ship Chart early is useful in order to be able to enter the Ghost Ship early, which is useful to farm rupees efficiently.
It is possible to enter Diamond Steppe early by superswimming. You will want to superswim to Diamond Steppe and get under the island before it has time to load. Kill your speed under the island. When the island loads around you, you only have to swim around to be brought up the island by the water on top. This is the fastest way to enter Diamond Steppe early, but is pretty difficult.
If you have high water waves on Diamond Steppe, there are a few spots around the island where savewarping puts you on the island early. This is very risky to go for. Once on the island, perform a wind waker dive to clip under the island and use the water on top of the island to warp up.
Get chest storage and sail to Diamond Steppe. You can enter the cave early by jumping from KoRL and gliding to the island. With chest storage, you can climb up the wall.
Using the mini tornadoes near Diamond Steppe, it is possible to gain height with the leaf and then glide onto Diamond Steppe. If you have the tingle tuner activated or double magic, you can even glide all the way to the highest level. This allows access to the Ghost Ship Chart without the hookshot in Bug Limit.
Here is the path that the mini tornado on the west side of the island follows, starting at the white and orange cube when you enter the quadrant: