Electrics in not my superpower, but if I recall, whether it was a battery charger or alternator on a car, the charging output voltage is always slightly higher than the battery voltage. Alternators for 12VDC I think charge at about 14V and if the battery is fresh it actually checks at about 13.5VDC IIRC. So for 8.4VDC charging, I think the battery nominal rated voltage will be less. So 7.2VDC sounds about right. Not 8.4.

The size batteries you need, in Amp-Hours (Ah), depends on the current draw of the light (Amps) and how long you want it to burn before needing a recharge.