Air does
not sit on top of CO2, they interdiffuse and mix completely (check the video below. Br2 mixes completely with air in about 30 minutes, and Br2 is about 3.6 times heavier than CO2.) If you cold crash with an airlock (or leaky fermenter), you
will get air into the fermenter. To minimize potential oxidation, package as soon as possible after cold crashing, and minimize any disturbance of the fermenter.
The only way to prevent air in the headspace when cold crashing is to have a vessel that is airtight. Something like a keg or SS conical with a spunding valve set to a few psi.
https://www.youtube.com/watch?v=_oLPBnhOCjM
Brew on