Coming out the warp tile, you can hookshot downward to the block. Hookshotting immediately will not save any time, but hookshotting to the left edge of the block can save up to 3 frames.

Note that unless Link is already facing left, a down+left input will always cause him to face downward, so you'll always want to hold down+left out of the warp.

If you're planning on using the cape or cane of byrna in this room, you'll most likely want to quickswap to those items ahead of time instead of going for this hookshot. This is especially true if you took the capedash in the previous room, since you'll need to allow for enough time to reset your cape cooldown.

These are common methods of getting past the firesnake on the bottom without waiting for it to pass.

Hookshotting to the right has a relatively generous (7-frame) window for avoiding the firesnake hit entirely and is generally recommended. Optimally, you'll start your hookshot as early as possible while still avoiding the firesnake hit.

You can also hookshot downward (or leftward) and intentionally take a hit. The frame window is tighter for ensuring the correct knockback direction (4 frames), and this costs 1 heart regardless of armor upgrades. Optimally, this only saves 1 frame, so it generally isn't worth going for. It's also less flexible in terms of routing the rest of the room, since you're locked into taking the bottom path.

Since firesnake hit detection only happens once every 4 frames, it's actually possible to avoid the hit entirely if you're lucky, saving additional time, but this is not reliable and only works for certain positionings.

Bonking off of the right-hand wall can potentially be easier to execute (provided that you don't accidentally grab the bottom wall), but is almost a third of a second slower.

If using the standard room start, this strategy is generally only possible when the second-lowest firesnake RNG causes it to turn around more slowly (moving upwards instead of bouncing left straight away). This will allow you to push the block in time to deflect its path without getting hit.

You'll want to hold up+left after the block starts moving, so that Link moves diagonally during the block push.

If the firesnake RNG does not allow for the fast strat, or if it's too tight to execute, one of these two strategies can be used instead.

The route through the lower path starts the same as a the fast path, but you walk around and push the block to the right instead. You'll most likely need to wait for about half a second after pushing the block to avoid running into the third firesnake.

Going through the middle path is also possible, and roughly equivalent in time. This gives you much less time to react and decide whether to go for the fast strat given the firesnake RNG, so it's only recommended if you don't want to go for the fast strat, or if you don't have the boots on hand. If you find that you have extra distance between you and the second firesnake, you can optionally dash to the left to catch up, but this usually isn't required. Optimally, you'll hookshot to the left as soon as the block starts moving to clip a full tile into the block, and ensure that the third firesnake has passed before moving up for the final hookshot.

Using an invincibility item will allow you to dash across the entirety of the lower path while avoiding the firesnake hit, guaranteeing that you'll be able to beat the firesnakes and continue with the "Fast Strat" regardless of RNG. In both cases, you'll want to start quickswapping to the hookshot immediately after clearing the bottom firesnake, to minimize magic usage.

A capedash will save somewhere in the range of ~0.75-1.5 seconds (45-90 frames), at the cost of ~10-15 magic points, which is quite efficient.

A byrnadash will save less time -- somewhere in the range of ~0.3-1.2 seconds (18-70 frames), at the cost of 16 magic points -- still pretty decent.

Keydashes are not possible on south-facing doors, so walking to the door after opening the chest is faster than dashing.