Many years ago, I used regular, alkaline batteries in my HP25 (not C) without problems. Of course, don't use alkalines and the AC Adapter/Recharger at the same time!
It's just my experience, but be very cautious; a working 25 is a treasure you should protect.
Rebuilding the battery pack with new NiCd batteries is a good idea, or eventually with NiMH modern rechargeables.
In any of these cases, please recharge your batteries in an appropriate EXTERNAL charger. NiMH recharging requirements are different from NiCd. Even with NiCd, there is a very high chance that any bad contacts (oxide, corrossion, dirt, etc) or other circumstances, will cause excessive voltage from the AC adapter to be applied to very delicate (unreplaceable) parts of your calculator, killing it in a fraction of a second. I have not enough time for a detailed explanation now, but please avoid any use of the AC adapter in your valuable machines.
Also, with a modern, external charger, it will be much faster to recharge the batteries.