How about, "No thanks, I'm just not drinking today".
If she presses you, maybe something like, "I simply decided. I just don't want to drink today, that's all".
If she's looking for you to enable her to drink, perhaps something like, "Well, pour me some water then, straight up and on the rocks".
Its honest, right? And no further explanation is needed.
I have to lean towards Carol though. If you two really are kindred spirits, then at some point I think you'll need to pull this out or else it will remain a barrier between you two. She's not responsible for your relapse. If you realize that then you can get her to realize it too.
Perhaps at some point you'll feel comfortable enough telling her, or perhaps not. Its *your* privacy. Consider though, if you did have cancer instead of alcoholism, would you be willing to tell her, and if so, at what point?
Just some thoughts.