One more thought-- you don't even have to say "I don't drink.". You could just say "No, thanks" and leave it at that. Just change the subject.
My son has chosen to make the step to become a vegetarian (like us), and that's what we've taught him to do to avoid unnecessary confrontations about his eating choices. If someone offers him meat and he doesn't want it, he does not say "I'm a vegetarian" unless he's prepared to get into a discussion or argument about it. He just politely says "No, thank you".