What do you mean by that?
If the humidity inside dry cab is not enough to condensate into water, that mean inside the dry cab is low humidity already.
If you said temperature inside dry cab is below the cold side of peltier temperature, so the humidity will not condense into water, that only probably happen in cold country, where humidity is already low and you no need dry cab anymore.
Wet sponge is on outer side of dry cab, as the water/humidity inside the dry cab is always condense by peltier element.
Regards,
Arto.