The fastest way to get to the first chest is to hookshot to its bottom edge. Dashing to the chest is slower than walking.

For the second chest, dashing is faster than even an optimal hookshot to the very bottom of the chest.

If continuing on through the eastern key door, a downward hookshot and rightward dash can be used as shown here. Opening the chest on the left second puts Link closer to the floor switch.

If the two chests have already been opened or are otherwise not being collected, an immediate downward dash can safely clear the moving spike on the way to the pot switch. For optimal movement you can hold left out of the stairs instead of down, but this decreases the time window for dashing past the spike from 10 frames to 4 frames.

Without boots, holding down out of the stairs will result in getting hit by the spike. While this doesn't actually lose that much time, it's faster and safer to cancel stair lag by moving left or right before starting to walk downward.

Canceling stairlag with a left input is technically optimal but has a much tighter timing window -- you must hold left for 1-3 frames before walking downward. For the rightward stairlag cancel, you can hold right for 2-7 frames.