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I had this wind up flashlight lying around, but the little NiCAD battery was completly dead. I didn't have any of the small button cell NiCADs lying around, but I did see a LiOn battery from a dead gadget in the junk box.
The nominal 3.7 V of the LiON is close enough to the 3.6 V NiCAD so I decided to try it.
The simple NiCAD charging circuit would ruin a LiON battery, but it did put out close to 5V under load, so another trip to the junk bin found a USB LiON charger.
After disconnecting the output of the bridge recitfier from the PCB, it was connected to the input of the charger. A capacitor was added for filtering and a 5.1V Zener Diode to protect the charger if you crank real hard.
The LiON battery was connected to the output of the charger and to the LED circuit. A fuse protects the wiring from shorts.
It has worked great. The LiON cell actually holds a charge over time, unlike the cheap NiCAD. It also has many times the original 80 mAh capacity and charges quickly. It might even be possible to cut a hole in the side of the case to allow USB charging instead of using the crank.