Hookshotting to the pot here can save up to 4-5 frames over simply walking and is recommended. No vertical repositioning is needed (provided that you entered the upper half of the previous portal).
If you entered the previous portal by simply holding diagonally down+right, you can theoretically delay the hookshot by one frame in order to allow for a single frame of down+right movement -- this will put Link's horizontal coordinate at 1634 and will result in the hookshot keeping Link grid-aligned, which can be better for exiting the portal since it prevents Link from clipping into the rail. This is not reliable though, since the required timing is frame-perfect.
Hookshotting will always avoid the worst-case horizontal coordinate of 165C (leftmost pixel of the portal) regardless of where the hookshot is used from.
You can dash all the way to the right past the pits if you are flush with the bottom wall. Link will simply grab the wall if facing downward, so you'll need to make a cardinal right input in order to face right before starting the dash. Be sure to release all d-pad inputs during the dash, otherwise the dash will be interrupted when crossing the pits. Optionally, the hookshot can be used to lengthen the initial dash and pull yourself directly across the pit, saving some time.
Without the hookshot, walking after the initial dash is essentially even with a frame-perfect dash (even without pumping), so dashing is not recommended here.
Typically the north-east portal in this room is skipped in this room via a bonk, saving over 4.5 seconds of time. There are 5 arrows available underneath the pot if you take the portal, but they generally take more time to pick up than the 5 arrows in Bob's Room and are usually only taken if many are needed for an upcoming Ice Armos fight, or if immediately needed for the mimics rooms in the Ganon's Tower climb.
The above animation shows the range of starting coordinates that work for the bonk (from 134F to 134C). Any lower, and Link will simply bonk in place. Any higher, and Link will enter the portal. As a visual reference, Link's shadow needs to be at least one pixel above the bottom edge of the left-hand wall.
Since there are 4 working pixels, generally this equates to a 3-frame timing window, assuming up is held as the dash-turn is initiated.
Without the pegasus boots, the portal can instead be skipped using invincibility frames. The fastest way to do so is by throwing a bomb and then walking past it so that the knockback pushes you toward the portal. Multiple strats are possible, depending on preference, hookshot availability, and the movement of the hardhat beetles.
Alternatively, a hit can be taken from one of the two hardhat beetles in the room, though this is slower and less reliable. This still saves over 2 seconds versus entering the portal.