Ok, you've got a carboy with negative pressure. At some point, somewhere in the process you're going to have to pull that plug to get the beer out and unless you are working in an O2 free environment you're gonna get air sucked in. It may be cleaner than the fridge air but pretty much all air is gonna have some bacteria floating around in it.
If you want to cold crash without any possible issue, here is what I suggest. Put a blow off tube into a jar of vodka or neutral grain alcohol and let it suck up a little of that as it drops in pressure. Won't hurt your beer, will prevent air from getting in, wont create a negative pressure environment and is sterile enough for our needs. I use vodka in my air locks, when I use air locks, so that if it sucks anything in, it won't be a problem.
I have been meaning to spray down the inside of my beer cooler with a mild bleach solution but haven't done it yet. For me, no problem cold crashing with foil but as they say in Internet speak, YMMV. Either way good luck.