How many Owen Wilson movies have you watched? Do you see how he handles situatons? The reason I'm asking is because you might just have to BS your way out. I mean if I really didn't want to do something and I really didn't feel like explaining my sensibility, I'd just mention that
"The last time I had a drink it caused this chain reaction where my cerebrospinal fluid built up rapidly sending me into autonomic dysreflexia and if I hadn't have been rushed to the ER that instant I might not have made it."
I mean it's total BS, totally believable if you say it right, and it might even be fun to say. After all, you feel pretty uncomfortable telling people that you don't drink, this can help get your point across and get you a little more comfortable.