To skip using the Command melody in the First Room, simply call Makar and then Item Slide to the opposite side of the room. DO NOT grab the door frame on the other side of the room, grabbing ledges will stop Makar from following you through doors 99% of the time.
In the room with Makar's cage, you can gain early access to the warp jar by shooting it with a Fire Arrow to skip some rooms. To setup the position, do two sidehops to the left after entering the room. Then line up the fire arrow and shoot it. Use the warp jar in the first room of the dungeon to get up onto the ledge.
For the most part, attempting to grab Wind Temple door frames is rather inconsistent. However grabbing the very right or left edge is about as consistent as grabbing any other ledge in the game. To start, face the right side column of the door to the south of the song stone blocking the way to the boss key. Using this angle, start an Item Slide back against the corner made by the song stone and the adjacent wall. Then when you have enough speed, use home buffering to hold forward on the control stick, ZL, and B all on the same frame. This will make Link Item Slide perfectly straight forward and get a jump out of it to grab the door frame. If Link jumps under the door frame, you were aiming too far left. If Link jumps to the right of the door frame, you were aiming too far right. Now Roll Clip through the door frame, Leaf around to the back of the door behind the song stone and land on the sliver of ground behind the stone. Then turn around, and open the door to get into the room with the boss key.
It is possible to access the Wind Temple Boss Key early with a variety of tricks. To start, position yourself on the turning floor panel so that the wind from the Leaf will barely hit the weather vane on the opposite side. Now blow wind using the Leaf and immediately roll backwards on the floor panel. Then do another roll angled up and to the left of the floor panel. Link will jump off when the panel gets too steep and from here pull out the Leaf. Hold ZL to target and Up-Left until facing the pillar on the right side of the room, all the while doing Leaf Pumps until you're close enough to the pillar to grab it. After you get on top of the pillar, shoot peahats if they're in the way, fly to the door frame on the right and Roll Clip through it. Now Leaf around to the back of the door behind the song stone and land on the sliver of ground behind the stone. Then turn around, and open the door to get into the room with the boss key.
This method is best done after using the Fire Arrow Trick to open the warp jar on the upper ledge. Once you've opened the first fan cage, jump down to the highest platform on the right. Kill any peahats that may interfere, place a bomb, and ledge clip OoB. Note that in order to clip, you must press the control stick away from the wall as soon as you re-grab the ledge (review video for reference). Immediately after Link slides through the wall, drop down onto the lower ledge. Now simply glide to the hookshot room and you will hit the loading zone.
By grabbing the edge of the right side on any door frame in Wind Temple (with the exception of the Boss Door) you can simply do a Roll Clip due to how far in the wall Link is when he climbs up. This is useful for skipping the key required to obtain the hookshot.
Alternatively you can Ledge Clip on the platforms inside the main hub room. After getting OoB just leaf to the hookshot loading zone.
Get into one of the corners near the spikes and place a bomb--it doesn't matter if it is in front of, or behind you. Wait until just before the bomb explodes and use a damage boost to reach the spike ledge. (If you placed the bomb in front of yourself you will need to jumpslash a second or two sooner.) This will give you temporary damage invincibility as well, allowing you to then skip past the spikes and get to the chest.
After you have obtained the hookshot, it is possible to clip out of bounds by backing up against a wall which has a hookshot target on it and hookshot the target at a specific angle. You can recognize the angle because the yellow target icon will be way to the right of the actual target on the wall
After you have obtained the small key above and the hookshot, head over to the right of the key room and hookshot up about three platforms. Backwalk so that Link grabs the ledge, move as close to the wall as you can, and then pull yourself up. Now place a bomb and use it to ledge clip OoB. Immediately after you've clipped and drop down onto the lower ledge. From here, backflip off the ledge and use the leaf to get under the second fan cage. Be careful not to fall too far or you will die.
The room with the wall of wind gusts where you'd normally have to use Makar to plant a tree and then hookshot it, can be crossed without the aid of Makar. Jump into the wind gusts and pull out the deku leaf to get blown left and then right. As soon as you are in front of the platform, put away the deku leaf and hold forward on the control stick to grab the edge.
In the room before the boss door, you can skip pushing the blocks by putting on the iron boots and continuously sidehopping past the blade traps.
Get next to the stone slab and sidle. Once Link is part way in the stone, stop sidling and roll until you are completely through. To get through with the fewest rolls possible, roll parallel to the stone.
After entering the room, charge up an Item Slide against the door and then release it forward through the narrow doorway in the middle of the room, and then jumpslash on top of the song stone. From here, Item Slide against the wall above song stone and you should fall through it
Diminish your health to 1/4 of a heart. Then, pick up the middle pot on the right side of the room and break it near the boss door. Zombie hover above the door frame and make sure to stay low. If you're lucky, as the fairies ascend, one of them will heal you. From here go to either side and perform a Ledge Clip to get behind the boss door.
If you break the song stone that's suppose to block you from normally entering the area right before the boss door, you can do an Item Slide paired with a precisely timed sword slash right before you are at the top of the stairs that preceed the song stone to grab the top of the Wind Temple boss door and then Ledge Clip through. Unfortunately this is slower as breaking the song stone requires bringing Makar all the way through the dungeon with you. If you Item Slide from the top of the stairs, you will simply jump against the wall.