If you're able to get the shoes 95% dry (following the suggestions in other answers), you can get them the rest of the way dry by spraying the shoes with a drying agent like 99% isopropyl alcohol. They'll be wet, but the alcohol and water form a mixture which will evaporate more easily than water alone. (It will work whether or not an azeotrope is formed.)
A small fan blowing on the shoes will aid the effect. It doesn't need high airflow.
Edit: A previous version of this answer indicated acetone could be an effective drying agent (if you're sure it won't weaken the rubber or fabric), but wikipedia indicates that doesn't work:
Despite its common use as a supposed drying agent, it is not effective except by bulk displacement and dilution.