To make sure that the battery will not be damaged by the recharging of the lamp measure the new battery voltage and the voltage delivered when the crank is spinned.

Attach a capacitor to the terminals of the old battery. Mount the gears and the crank. After spinning the crank a few times measure the voltage of the capacitor with a multimeter.

Measure the voltage supplied by the new battery or read the datasheet of the battery. This voltage should be roughly the same as delivered by the crank.