One application of alcohol and water will not dry out ivory. In fact, an alcohol/water mixture is often used for cleaning by conservators.
The reason that a water-alcohol mixture works is that the spores, which are protected from most kill methods when they are dormant, become susceptible when they get wet. If you want to know more about mold in museums, Mary-lou Florian has done extensive research on mold and written several books on the topic.
I am on the committee that is responsible for the MuseumPests.net web site. So far, however, we have been concentrating on insects and vertebrate pests. We are currently working on a mold section. Stay tuned.