"puff of air" is correct and usable in written English.
You can use it to describe a short, sudden burst of air. For example: "My daughter was surprised by a sudden puff of air coming from the fan."
"It's just a puff of air".
Feel that puff of air around the ears?
The aspiration accompanying stop consonants consists of a small puff of air.
A word that means, if we're being literal, a puff of air.
A puff of air blew across my face, bearing the unmistakable aroma of orange juice.
And then, there's a sudden puff of air on the back of your neck.
Bekinschtein et al. (2009) presented PVS patients with a tone followed by a puff of air to the cornea.
The "p sound" occurring after the /s/ is unaspirated (i.e., it is pronounced without any accompanying slight puff of air).
Or they might fail to articulate the little puff of air preceding the actual tone of a tuba.
One, by Cortney Davis, a nurse practitioner, is a poem: "Pearly, uninformed, it waits/ for the otoscope's puff of air".
