All web maps must have a basemap. It's what sets the coordinate system of the web map. It is possible to add a layer and make it the basemap, effectively making a web map without one of the default basemaps.
the only other thing I can think of that 'may' work is to author an empty map service and make it the basemap. It may cause other issues, like what is the extent? No guarantee it will work.
Thanks,
Mike