Please be cautious with using different batteries on your Electron. The battery you have with 3 wires likely has a temperature sensor embedded in it for safely monitoring the battery temps while charging. Check the max allowable charging rates without temperature sensing for your battery. The Electron charges the on-board battery at a 512mA rate. It’s also not clear what protection circuitry is in your battery vs the one supplied with the Electron. Be careful not to short your battery. Just to be clear, the battery you linked at Sparkfun is not the same one supplied with the Electron. The 2 pin JST connectors you linked should match the receptacle on the Electron… this is the standard JST PH-2.
I asked CookingHacks about their battery and they said the documentation for the battery states that it can be charged up to 1A. So there shouldn’t be any issues. Thank you for your help @BDub