for bottling..
if you allow a small amount of air in to your carboy while you cold crash it, the existing Co2 in the Carboy is heaver than the air going in. this air will sit on top of the Co2, So just use the cotton ball idea to filter the air going in, or just use a solid bung.
CR-
The "CO2 blanket" has been debated before. Yes, CO2 may be heavier than O2, but gasses diffuse and mix. Without a one way valve or continuous purging, that headspace will eventually be air, a combination of O2, CO2, nitrogen, and whatever else is floating around in your environment. That probably doesn't matter much if you're cold crashing over a few days. The potential for infection and oxidation is there, but it's a minimal risk, from my experience, in my environment. That's why I don't do long term aging in buckets or carboys and why I don't transfer to secondary. I try to minimize how much I disturb the beer and prevent splashing around. Afterall, you have to get O2 into solution for oxidation to really have a significant effect on your beer.
As for the solid stopper. It may work sometimes, but it may suck the stopper in too far. I've never had one sucked all the way in, but I've had one get sucked in so far I couldn't get it out until I warmed the beer again. My whole point to cold crash was to drop yeast and add gelatin. Having to warm the beer up again meant I had to then cold crash again, this time with foil, so that the gelatin would be most effective. A carboy cap or a stopper with a lip around the top and some saran wrap could do the trick here if you want to completely seal it off and let it create a vacuum of sorts.
The cotton ball in the airlock is a good idea. Many probably already have cotton on hand, just like they do foil, so it's a quick simple, solution. For the overly paranoid, you can spray or soak the cotton in sanitizer first.
My whole point is, without splashing the beer around, either on the hot side of things or post fermentation, I have not noticed oxidation. Surface contact with air is probably not that bad over a short period. Long term aging that way may create a problem.
Just for kicks and to overly complicate this matter even more, what about filling a sanitized balloon or rubber glove with CO2 and flooding the head space with CO2? You can place the balloon over the opening and when it begins to suck in, it's pure CO2 over your beer. That's a bit rediculous in my book, but hey, if I had the means I would probably try it just for fun. But it would have to be with a rubber glove, because that would look funnier.