If you really don’t want to explain, fill a beer bottle with water and drink that all night. I frequently have one or two beers then do this for the rest of a party, and feel great the next day.

I learned to just carry around a half-empty bottle if I was at a party. As long as you had something in your hand, it wasn't a topic.

My personal problem is that I can't help drinking that bottle in the lapses between conversation or whatever. So filling it with water is perfect for me.

Same. Drinking whatever is in my hands is almost a tic. Filling it with water is an excellent idea!

Don’t mind that at all. It’s fascinating to see how people react to one’s explanation. Very polite people will actually ask if I am okay if they drink around me which of course is no issue whatsoever.

I've rarely had to say more than "no thank you". It's never been awful.