You can use two LJAs to cross over the first room without using an Ooccoo. For the first LJA just wait until the boomerang is over the void, for the 2nd you can hit the pillar to make the boomerang come back faster and hence be quicker.
Opening the door to the hub of the dungeon from far enough way will prevent Link from hitting the trigger that activates the fan blocking the way to the boss key. This can be done by opening the door carefully as wolf. This saves around 1:30 for Any% and All Dungeons, 5 seconds in 100%, and some time No S+Q as well.
You cannot hit the trigger for the fan while transforming, so it is safer to transform right before the door so the animation will bump your backwards and in the correct position. This is slightly slower than approaching the door as wolf, but is much less risky.
This method involves transforming to wolf before reaching the door, which can save time on movement but makes it harder to avoid hitting the fan trigger.
When you open the first small key within City in the Sky, a cutscene trigger is added at the end of the bridge that you came in from, and your savewarp point is changed to start you off next to the small key chest until the cutscene is triggered. This savewarp spot is incredibly convenient because you return to this room immediately after obtaining the Double Clawshots, which saves some backtracking.
After obtaining the first small key, head back outside and cross the bridge. Target the last peahat and sidehop onto the banister on the right on GCN (it will be the last broken chunk before the staircase). Jump to the next banister then head back into the dungeon through the broken grate window, staying clear of the door at the end of the bridge.
Alternately if you don't feel you will make the sidehop before the wind starting blowing you can clawshot onto the last peahat, look towards the window then drop and jump attack to get past the trigger. This is slower however.
Instead of going the intended route past the fans, you can go to the right and simply LJA over to the door.
There are many ways to get through the block room before the double dynalfos. The fastest method for GCN is to roll around the right side, LJA using the tileworm, and then boomerang LJA to the exit. This method and several others for GCN are covered in the tutorial video below.
Run straight for the center of the platform on the other side of the room, and perform a spin attack. This will knock the two Dynalfos off of the platform. Quickly target the vines with the clawshot, and grapple to them before the cutscene begins.
It is possible to skip turning on various fans in this room with a well angled jump with an Ooccoo. Use the 2nd fan to get atop the broken wall with Ooccoo, angle yourself towards the ledge, hold target, and then hold forward to jump. Then, drop Ooccoo at the correct time to grab the ledge. If you fall straight down instead of jumping, it means you were angled too far right and walking into the wall; if you do fly but are too low to grab the ledge, it means you jumped off too low or took an unnecessarily long flight path.
This is slightly faster than picking up the Ooccoo but costs 2 hearts.
This grate clip skips the outside section of the traditional early boss key sequence by doing a skewed clawshot shot through the part of the grate that's missing hit detection, onto a small grate above.
Alternative setup by Glubbers: here
Setupless concept by bewildebeest. The first visual cue is at the tip of the triangle shown in the video. After Link begins to fly towards the target, hold down and the Clawshot button so that Link descends a consistent amount. Aim for the small grate as normal.
Instead of clipping through the grate outright, Wii can use the reticle displacement in third person aiming to find the upper grate above. Note that for this to work, Link has to be dangling from the grate with his right hand and clawshotting with his left.
It is possible to skip turning the northern fans on on the way to the fan tower. Clawshot onto the first two fans high up in their clawshottable areas and from above so that Link grabs the tops of the fans. From there, use LJAs to reach the exit door as shown in the videos below.
An LJA to skip the three clawshottable pillars is possible but very precise.
Roll 4 times to stand on the very edge of the blocks, then aim in line with the wall and throw the boomerang as high as possible. LJA as soon as the sword is out. Roll 3 more times and clawshot the peahat to make the cycle without waiting. Roll towards the north edge and target the wall, then LJA onto the broken wall of the island with the poe, B-Charge the poe from the wall and collect it. If done correctly, you should have enough time to clawshot back. It is then possible to LJA across the gap to the heart piece chest.
It is possible to skip transforming wolf and going on any ropes in the area before the boss key room. To do this stand next to the door and clawshot the vines, you should barely reach. From here you can stand on the edge and target on the ceiling above the door and LJA across, this works because the boomerang is over the door frame which is higher ground
Using a bomb arrow to hit the top fan tower switch from the floor can save around 8 seconds over ascending the tower normally. Using two bomb arrows can save even more time but is extremely difficult.
Roll through the first two fans. Then to get past the last fan, equip the iron boots, and quickly sidehop across the falling blocks.
Since boomerang Long Jumps can't be done on the Wii version, instead throw the boomerang at the keese conveniently located near the gap. As the boomerang starts to return towards you, target the keese in order to do an LJA. Repeat this process to cross the final gaps.
It's possible to LJA to the HP chest without using the boomerang. Simply stand near the edge of the block, target the Peahat, and when its in position jump attack to make it across.
With precise clawshots, ledgegrabs, and arranging them to aim with the clawshot arm closer to the final fan, it's possible to get across without using LJA's of any kind. This can be marginally faster than turning the fan on, and is much riskier.
It is possible to CAD the cylinders in the compass room by falling off the chest, then interrupt the CADs with bombs to position the cylinders in precise locations. It is then possible to perform Jump Strike Moon Boots to reach one cylinder, LJA to the next, and finally clawshot to the upper floor, skipping the small key on the west side of the dungeon.
Please note there is a faster way to complete CitS by getting the Boss Key Early.
This saves 5 seconds. Stand on the very edge as shown in the video, aim just to the left of the structure and throw the boomerang, if you LJA as soon as possible you will land as shown and be able to clawshot up skipping a clawshot target.