Note: Learning the Wind God's Aria before beating the Forsaken Fortress 2 will crash the game due to wrong animation sets. See here for more info.
It is posible to enter Gale Isle and learn the Wind God's Aria without the Iron Boots or without the Skull Hammer. This can be useful for routing purposes.
Contrarely to obtaining the Earth God's Lyric early, there are no complications to learning the Wind God's Aria early (no possibilities of softlocking when entering the island with Makar later on)
You can skip the iron boots requirement by pulling out the Wind Waker, walking a little towards the statue you want to break with the hammer, then pulling out the Wind Waker again, and so on. This works because you are not vulnerable to strong winds right after pulling the Wind Waker. This allows you to get really close to the statue without Iron Boots. Use the Hammer jumpslash to break it.
With Chest Storage, from the boat, you can leaf and land on one of the pillars on the eastern side of Gale Island. You can then climb up it and leaf to a higher ledge on the island. With Chest Storage, you can simply clip through the island somewhere on the back and enter the loading zone without the hammer. You can then proceed by learning the Wind God's Aria.
Zombie Hover to the higher ledge of the island and use the tingle tuner to heal yourself. You can clip OoB by simply hanging from a ledge close to the wall and letting go, no need for a roll clip or a ledge clip.
To do this without the Tingle Tuner, zombie hover to the pillar on the western side of the island that has hearts on it and then leaf to the island once healed.