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Yeah, I tend to leave the airlock out until I've moved the fermenter to it's resting place. Similarly after fermenting, although sometimes you get enough gas pressure inside that when you lift it it doesn't displace as much (I carried 25 litres up from the cellar last night without removing the airlock and nothing got sucked in).
I wouldn't worry too much about a few drops of Milton. Many people use diluted Milton or bleach/vinegar as a no-rinse sanitiser, so in low doses it's unlikely to have any effect.