I wouldn't recharge your vape if it doesn't seem like it can be. It's safer not to risk it. If you want a vape with a rechargeable battery
Welcome to Maker Pro!

You're concern is admirable.
Looking forward to your continuing contributions.
His battery charger can accommodate a multitude of rechargeable battery chemistry's as well as automatically ; totally programmable hence the flow chart. All that is needed is the specifications for his specific rechargeable battery chemistry with that information you just chug and plug. Meaning RTFM.
The charging algorithm is capable of manual input or totally autonomous operations. For example
Voltage and Capacity Compatibility. Charging Current.
Over current over voltage sensing protection
Temperature sensing.
Efficiency and Energy Savings