When I used to brew, the smell of the fermentation coming through the airlock was divine. I would think you stand a pretty good chance of passing some airborne yeast cells through that airlock. You DO NOT want airborne yeast cells around your cheese-making operation.
Very ambitious project, but I would definitely want to segregate the two hobbies. I recommend a separate 4.x cu ft (or larger) fridge with its own temperature controller to maintain your sanity and permit the development of quality cheeses. There are certainly enough potential problems in making cheese without handicapping your efforts.
And, yes, I would second the need to build in adequate long-term aging space. Some cheeses can require 12 month minimum aging at cave temperatures (Cheddar, Beaufort, Gruyere, Manchego, Gouda, Parmigiano, etc.). While those are aging, you'd still want to be able to make shorter-term cheeses. That takes shelf space. I've found that my two small caves ("night & day") require cheese-juggling sometimes to be able to fit cheeses in. As cheeses hit their aging target they can be moved to a larger, colder fridge for continued longer-term storage.