First of I hope it is sanitised water in your airlock. I just use cling wrap over the top of the fermenter kept in place by an elastic band. I have been down the route of balloons and adding gas to the fermenter without any noticeable difference. Twice I have accidentally left a sealed lid on the fermenter while crash-cooling but the amount of co2 being sucked into the cooling beer just made a couple of big dints in the fermenter.
Cling wrap while fermenting allows CO2 to escape, so it obviously works in reverse in cold-crashing conditions. However, with good head space, it is doubtful the oxygen gets into the beer. If it does, I have never experienced it. It is much like bottling: When we bottle, there is air in the headspace of the bottle, so there is some oxygen. Does this small amount of oxygen oxidise the beer? Yes, but it can take years.
As homebrewers, we do our best to avoid oxygen but oxygen is more problematic for commercial brewers. Our bottles get filled and stored in a cool, dark place and not shaken around as do deliveries of commercial beer.
So don't worry about oxygen ingress during the cold crash it will turn out you are most likely worrying for nothing.
https://byo.com/mr-wizard/oixation-while-cold-crashing/#:~:text=While a small amount of,the headspace is relatively small.
