I'm not entirely sure of the physics of this, but I believe the fastest way would be to create, in effect, a "bullet" of air. If you compact the area of the wind down to the size of a bullet, and blast that air extremely quickly at someones head, it should just tear right through their brain, killing them instantly.
This can be seen in real life, as actor Jon-Erik Hexum accidentally killed himself with a blank loaded gun, after firing the pressurized gas into his head. https://en.wikipedia.org/wiki/Jon-Erik_Hexum#Death
The difficulty is that your "air bullet" will lose pressure and dissipate quickly as it flies through the air. This is fine if the wind magically maintains pressure and precision the whole flight (which is perfectly fine in a fantasy setting), but if it doesn't, they could cup in their hands a metal spike or create a spike of ice by cooling the atmospheres humidity and fire that as a make shift projectile. Depending on the degree of control over the wind, they could adjust trajectory of the projectile mid flight, to potentially kill multiple people!
Taking this further, if they can create a thin edge of wind, they could fire out air blades, to slice up their opponent, effectively like throwing the blade of a guillotine at them. This could be used for gory effect, like to behead someone at a distance, but perhaps is a skill reserved to the most masterful mages, as it in theory would be more difficult to create the right shape of the projectile with their hands, and not blow up their own hands by accident, vs using a physical projectile.