I don't think you could have absorbed enough alcohol in a minute to affect you at all. I still use Listerine mouth wash from time to time, which has alcohol in it. I've never felt any different or gotten any cravings from it.
In the end it's up to you. You ultimately decide what falls under sober behavior or not (within reason of course!). Some people would never use Listerine, but for me I don't consider it to be taking alcohol since I don't ingest it. But I really don't think that an accidental mouthful of remedy would give you a blackout, even if you're very prone to them.