Let me say first that I am not a chemist. When Robert posted something about surfactants I thought he was talking about a Beach Boys movie.
I estimate that my 2 gallon (7.5 liter) headspace will shrink by 7% when cooled from 70 F (294 K) to 34 F (274 K). That is a volume of about 16 oz (500 ml), not a trivial amount. That air will mix in the headspace, exposing the beer to a 7% air mixture for days. Of course the exposure will be at a low temperature, so the chemical reactions will all be slower. There are other phases of the packaging process where the beer can be exposed to pure air but only for a few seconds or minutes. Which is worse: exposure to 7% air at 34F for days or exposure to 100% air at room temperature for seconds or minutes? I don't know, but my gut tells me that the longer exposure would more than compensate for the reduced temperature and concentration.
Using a rubber balloon should work, provided you put it on at the right time. Too early and it would overfill and explode or blow off. Too late and it would not collect enough CO2 and would collapse during the cold crash. Now I know that if that happens, though, I can just jiggle the carboy to release enough CO2 to partially inflate the balloon again. I will try that experiment on my next batch.
Your math is also way off. As water (which is the majority of what beer is) cools from 20 degrees Celsius (70 degrees F) to 4 degrees Celsius (39 degrees F) it shrinks about .00021 ml per degree Celsius. So the total shrinkage for 7.5 literrs will be about .0252 L or roughly .8 ounces. No where near the full pint of liquid in your calculations. Now as the water (or beer) is further cooled from 4 degrees C (39 degrees F) to 1 degree C (34 degrees F) it actually expands due to the unique properties of water that allows ice, a solid, to be less dense and float on top of water.
The gas contracts too. Not sure about the total volume involved, but I know from experience that crashing a closed fermenter from ~68°F to ~33°F results in a pressure drop of between 2-3 psig. Which on a glass or plastic vessel could be quite dangerous.
But in a fixed container, your volume remains constant. If you are talking the gas only, the density of the gas will increase, but its volume will remain at the 2 gallons of head space that you started with. You would have to calculate the change in density of air in order to figure out the additional oxygen exposure. The difference in air density from 20 degrees C to 0 degrees C is 0.089 Kg/M3 or 0.089 Kg/1000L or 0.000089 Kg/L. So in 7.5 L of head space, you get an additional 0.0006675 Kg of air. Air being made up of only 21% oxygen, your additional oxygen exposure would be 0.000140175 Kg or only 0.140175 grams of O2. Basically a negligible amount.
A pressure drop of 2-3 psi is also negligible. That change in pressure won't burst a glass carboy and will only affect the weakest, thin walled plastic ones.