The bottom line is that most people simply won't care. Your drinking, while important to you, is merely a curiosity to others.
I quit 4 months ago.
I didn't tell anyone at work. it's none of their business, and there is very little upside for me in their knowing the real reason. All work places have some element of competition and perception does truly matter. I certainly didn't want to run the risk of anyone using it against me. When offered a drink, I simply said "no thanks. i'm good." If pressed, I'd say "I'm trying to lose weight".
I did tell my 3 closest non-work friends. They were surprised, and asked more questions which I opened answered. I was glad that they asked a lot of questions, because it showed that they cared.
Best of luck!