How related are NiCd and NiMH chargers?
Its possible but hard to answer without knowing the charger topology.

NiCd can be handle very high charge/discharge currents.  Such charge currents could damage a NiMH battery.

Now it MAY be OK, not all NiCd chargers are of the high current/peak detect variety, sometimes called "Rapid Charge".  

Some are simply timer based in which case they will very likely undercharge a NiMH battery.

Still other NiCd chargers are "trickle chargers" made to slow charge overnight, such a charger would work with NiMH but would likely take a very long time to charge since NiMH batteries generally have a much higher capacity.

Yet another charger type is the "smart charger" which monitors the battery as it charges and adjusts its charge rate, stopping or going into a trickle mode when the battery is determined to be full.  The "full" trigger and charge profiles are different between NiCd and NiMH so I would assume this type would need to be modified (possibly with new firmware) to handle NiMH batteries.

EDIT: Ancillary question: are you sure switching battery chemistry is a good idea for this application?  The mAh rating doesn't tell the entire story of battery life.  If the device is high current then a NiCd battery may last much longer than a NiMH battery even though the NiMH battery likely has much higher mAh rating.