Never use an AC adapter without good, working, NiCd batteries in place, alkalines seems to be a good choice in your case (no warranties, but it was OK for me many years ago). Alkalines will last for many hours, opposed to the 2 hours typical with rechargeables.
If you decide to use rechargeables, it is advisable to recharge them in an external charger, not to risk your valuable calculator, since these are very sensitive to overvoltage events that the AC adapter may cause. An external charger will also allow you to use NiMH AA batteries, which last longer (hold more charge) than NiCd.