'No thanks, I don't drink'
Or
'I'll just have water, thanks'
Or
'No thank you... I'm good!'
Or
'Nope, I'm not a drinker'
Or
'No thank you! I'm not drinking'
Or
'None for me, thanks!'
Or any of a hundred or so other possibilities. Doesn't really matter. I used to get hung up about what to say, what people might think, how to 'spin' it, what they might say, how to respond to that....
Turns out I really was wasting my time worrying. Most people really didn't care that much and most of those who did take notice were friends who were also heavy drinkers or alcoholics and their comments were always along the lines of 'wow... I sure wish I could do that....'.