It is possible to prevent fall damage in Breath of the Wild by abusing the force unequip functionality of this game.
After jumping off, hold R (standard) to pull out your melee weapon and get into the throw animation. Before hitting the ground (not precise), let go of R and immediately force unequip your weapon with the D-Pad.
The animation of Link putting away the weapon will cancel the fall damage.
This can also be done by force unequpping your shield.