As the deku leaf is one of the most useful items in the game, the only time where it would be skipped is in a Low% Speedrun. Skipping the deku leaf is primarily based upon using zombie hovering in the areas where the deku leaf would normally be used, which entails always making sure that your wallet is full of rupees so that you can purchase red tings, 20 rupees each, to heal yourself.
Obviously because you don't have the deku leaf, you cannot enter the Forbidden Woods in the traditional manner. Instead you will have to zombie hover over to the entrance and heal yourself with a red ting. If you have already obtained the Bombs Early, you can save yourself some rupees, if not, you can use a deku baba to damage yourself and start your hover. However, there is a high chance that if using the deku baba that your angle will be altered. Otherwise, you will have to purchase a Tingle bomb to start your hover, which costs 10 rupees each.
The 2nd and 3rd rooms of the Forbidden Woods usually require the leaf to go through. It is possible to skip the requirement by zombie hovering and healing with the tuner, once again.
Since the Deku Leaf gives you the magic meter by default, you will not be able to obtain it before the Forbidden Woods. However, since items such as the fire and ice arrows require magic power, you will still need the magic in order to complete the game. To obtain the magic meter, sail to Two-Eye Reef (quadrant D7), and defeat the Big Octo for the double magic meter. Note, you cannot sail to the quadrant before beating the Forbidden Woods.
Note: Since it is currently impossible to skip both the Hero's Bow and the Deku Leaf at once, skipping the magic meter is not an option as of now. This is because skipping the Light Arrows in Ganon's Tower requires the deku leaf.
Once again, you can get past all the deku leaf requirements using zombie hovering. It is interesting to note however that you can skip the deku leaf requirement in the first room using Spring Jump Storage.
To skip the leaf in the 2nd room without hovering, play the Command Melody to get control of Makar and fly above the gate to land on the other side. Then step on one of the switches to rotate the gate.
Although Fire and Earth trials are easily completable without the deku leaf, Forest and Wind are a different story. With the Tingle Tuner out of commission while you're inside Ganon's Tower, you will have to find another way to heal yourself out of a hover.
In the Wind Trial, there are pots near the end, and the very leftmost one has a heart inside of it. When you enter, align yourself to this pot with the telescope and begin your hover. When you get close, you'll need to hover low enough to make a bokoblin aware of you and follow you around. You need it to break the pot, hope that the heart lands in a spot below you, and drop down onto it. From here, just hookshot up and fight Molgera.
For the Forest trial, this one gets even trickier than Wind does. There are 2 pinecones at the end of the tunnel, and the one to the right conveniently has a heart drop. Align yourself to the pinecone. Start your very tedious hover until you get near the pinecone. Once you reach the pinecone, drop a bomb, get hit by a Peahat, and immediately continue your hover until you're above one of the heart drops. Drop onto it and fight Kalle Demos to your hearts content.