Few devices that i converted to Li-ion batteries from ni-mh i made posible to charge with external Li-Ion charger using these connectors:
https://www.ebay.com/itm/10PCS-Batte...gAAOSwxQhaqMil
If you dont manage to find another solution it could do the job for you, should be pretty easy to make a port in the plastic for the small jst connector.