It is possible to get to the highest island without going through the cave which entrance is located on the small island. To do so, first get chest storage and then maneuver your way to Cliff Plateau (either by sailing or by superswimming). With Chest Storage, you can aim the hookshot inside the island and hookshot to the chest containing a Treasure Chart early, skipping the cave completely, cave that doesn't have anything required for 100%.
You can also skip the cave without the hookshot by climbing the tree with chest storage, then jumping towards the big island and with precise leaf pumps and a precise leaf cancel, you can grab the ledge and make it to the island without entering the cave. Because climbing the tree with chest storage is extremely precise, this is usually not done in RTA speedruns.
You can also skip the platforms inside the cave with good leaf pumps.