Way I see it as soon as you remove that airlock, then lift the fermenter you are creating and easy way for nastys to enter. I would rather that few mls of sterilized "no rense" sterilzer than a gulp of no so "fesh air".
I still try not to move them as its well documented that oxidation can = poor brews. but i have in the past doing it very carefully to minimise gulping and sloshing without impact. The best method seems to be the board under the fermenter, get a mate to help you is prob better still.
I brew in the fridge and each time I take a S.g.Read or move the fermenter, I just unscrew the lid so the airlock goes level.
Just remember to tighten it again.
If it still fermenting when you move it there is no need to worry about aeration or bugs inless you drop the darn thing.