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I opted for a Panasonic NCR18650B, choose the version with solder tabs, otherwise it will be a pain to solder wires on the battery and you'll probably go out from the factory dimensions. From the benchmarks it looks like a very good battery, time will tell.
Fit the new battery, cut the leads to the needed length, pay attention to polarity. You may need to enlarge leads holes in the plastic case with a cutter to let standard battery leads thru.