^ I gotcha. Yes, as the liquid contracts, the ambient gasses will be sucked into the fermenter. You clearly know that your airlock sanitizer/liquid is going to get sucked in, so replace that with a piece of sanitized foil over the bung. Your beer has created c02 in that headspace (as you know), so any 02 sucked in will settle above that c02 blanket. I recommend you cold crash near where you rack so when you move your beer, you won't slosh too much and mix that co2 and o2 layer up.
Another options which I do frequently, is to put a #0 stopper in the bung and cold crash it. The Better bottle will warp as the liquid/gas contracts, but then you can move it for racking without fear of mixing the co2/02. You can even burst some co2 right at the bung as you remove it so the ensuing "suck" from the fermenter will be sucking in c02 rather then 02.
Hope this helps. The big thing is to try and not disturb that layer of c02 over your beer. Cold crashing is a 24-48 hour thing, so if you don't disturb that layer and use the foil method you won't be oxygenating your beer. I mostly use the stopper method and deal with the temporary misshaping of the better bottle (it generally bounces right back) but if you do this too many times, you will notice the shape tends to persist a bit. I don't really care about that personally, but some will.