Welcome to SR!
I agree with Flutter 100% that people really don't care if you are drinking or not. I have found that there are many folks that don't drink, and the ones that are drinking do not care if I am or not. It is so much easier to say no than you might think. Good advice from others on small fibs to tell as well.
I would also ask yourself how good you have been in the past with just having 1 beer. You mention that you think you could just have the one beer because of the situation. It sounds like you have tried this before and it didn't work. I imagine there is more risk of people realizing you have a "problem" if you choose to pick up that first drink (which usually leads us to the second, third, etc) than if you simply say, no, thanks.