In general I would advise against riding in malls except when necessary, because the rules of the road are not adhered to as well. For one thing, you're much more likely to find someone driving on the wrong side of the road in a mall parking lot than on a "real" roadway.

Having said that, there are exceptions to all general guidelines, and your circumstances certainly seem to qualify. Not only is the mall small and generally quiet, but the alternative is highly unpleasant.