If you are dealing with desiccated mummies I would not recommend an active
system for the display cases.  Reasonably well sealed display cases with a
preconditioned humidity buffer (I recommend 35 x 5 %RH) will do the job.  If
it is a long-term display then I would go for hermetically sealed cases with
an inert gas atmosphere (nitrogen or argon).  Mummies that have not been
desiccated will require different conditions, which can also be provided by
passive systems.
 
Frank D. Preusser