When dashing downward, doing so further to the left will allow for more efficient (and easier) diagonal movement into the door. Note, however, that being on the leftmost pixel of the hallway will cause Link to miss the switch trigger entirely.

Without a sword, dashing is generally not recommended here. It can theoretically save a couple of frames over walking, but only if your 4px/frame dash movement happens to stop on the top edge of the switch. If your y-coordinate is suboptimal when you start the dash, you end up losing time instead.

In the second part of the room, holding down-left out of the door will allow you to save time by avoiding the switch trigger.

Walking around the Popo is optimal if it's on the top or bottom of the hallway, but this is not possible if it's blocking the middle of the path.

When lampless, a common strategy is to have Link's sword held out to the left to poke the Popo in the hallway and use this as an opportunity to drop the sword charge without having to do a spin slash. Positioning Link closer to the middle of the path can ensure the poke regardless of the Popo's movement.

The audio cue / screen freeze from the small key door opening can be used to determine when Link is in position to exit the room. Note, however, that Link must be facing left in order to trigger the door.