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.
After crossing the first room of the dungeon with 2 LJAs, transform to Wolf and approach the door leading to the main room carefully. If you open it as early as possible (don't rush!), the trigger starting the fan will be skipped and therefore the fan will not spin. Now just clawshot the vine on the side of the pillar, climb up and clawshot up to the room over the fan. From there just proceed with the usual way to the Boss Key (you can just grab it cause the fan is turned off).
This saves around 1:30 for Any%.
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. Clawshot onto the last peahat, look towards the window then drop and jump attack to get past the trigger.
Instead of going the intended route past the fans, you can go to the right and simply LJA over to the door. Note: with gate unloading, it is slightly faster to roll across the left side of the room through the fans.
After entering the room with the unloaded gate you can go down to Aeralfos' room by using an LJA. The aiming is rather precise.
If you land on the platform above, just backwalk and jumpslash towards the door.
*Please note there is a faster way to get to Aeralfos by unloading the gate
Simply use a few Long Jump Attacks to cover the gaps without waiting for the updrafts to disappear. You can also do two Double LJAs that don't save any time.
*Please note there is a faster way to get to Aeralfos by unloading the gate
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.
*Please note there is a faster way to get to Aeralfos by unloading the gate
It is possible to skip turning on various fans in this room with a well angled jump with an Ooccoo. To do this use the 2nd fan to get ontop the broken wall with Ooccoo, then angle yourself towards the ledge and jump. If you just fall down it means you was walking into the wall and if you can't grab the ledge it means you weren't angled enough. Remember you need to drop Ooccoo at the correct timing so you can grab the ledge.
For unknown reasons this is way harder in the HD remake cause Link will just drop off the ledge after 1 frame frequently. To prevent this you have to gain more height of the jump overall and let go of the ooccoo earlier.
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.
Please note there is a faster way to complete CitS by getting the Boss Key Early.
Once outside after the room with the giant deku baba it is possible to get over the wall without waiting for the Peahat with precise movement. To do this roll 4 times and end on the very edge of the blocks, then aim in line with the wall and throw your boomerang as high as possible and LJA as soon as your sword is out. You can then roll 3 more times and make the cycle without waiting.
You can also LJA over to Heart Piece Number 2 from the very edge by aimming at the spot on the wall.
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.
It is possible to clawshot through the floor up to the boss key. This saves around 10 seconds or so over going outside. Clawshot the left square of the diamond shown in the video, then clawshot to the target through the floor. The initial target is fairly precise.
After getting the boss key you do not have to start the fans to get to the north tower. Instead when you clawshot the very top of the fans from higher up you will grab the ledge and be able to climb on top of them, from here you can use LJAs to cross.
Instead of the double LJA you can clawshot to the third fan and LJA from there. This is only a bit slower.