If someone doesn't support your decision not to drink - for whatever reason - (s)he's not a true friend. It sounds mind-numbingly simple, but it really is that simple. There's no reason to cover up not drinking. There's nothing abnormal about not drinking. Plenty of people do it and don't think twice about it. They see those movies from the 40's where the first thing people ask when someone comes to visit is "would you like a cigarette or a drink?" and yet it goes in one ear and out the other. It never occurs to them to smoke or drink. There are tons of people like that.
I don't feel like I need to explain to drunk people singing karaoke why I'm not drinking. But then again, I never put myself in that situation.