The alchole doesn't evaporate. In fact, if you leave the lid off a bottle of booz, the water will evaporate leaving behind a beverage that is even more powerful. The alchole is disipated by heat. Wheathe you bake it or cook it on top of the stove, heat makes the alchole go away. Hay, that's how an internal combustion enjun works.
I have been associated with many recovering alcholics in my life. Most of them can tollorate a smidge with out getting re-hooked. The amount of booz in a cake that is cooked with it is usually a very safe bet. However, not so with a cake, like my Sherry Cakes, that are saturated with the booz after the cake is made.
With someone who has a very severe problem, it is usually sort of"guilt by association." It's not the actual minute traces of alchole that may be present, but the flavor that triggers all the old responses.
Like someone else in this thread said, I'd go with another cake.
And, while still on the subject: when people are entertaining non drinkers they are almost always thoughtful enough to provide a non alcholic drink, however, it is usually sweet: a punch, juice or soda of some sort. Try offering a non sweet alternative. Seltzer or club soda over ice and fruited with a twist of lemon or lime is very frefreshing and looks lovely and special as well. Try seltzer with a splash of tomato juice, v8 or snappy tom. Fruit it with a sprig of freshdill weed and a slice of cucumber.
Your non drinking friend will be most appreciative.