You shouldn't have to go trough those 6 pin connector.
Some battery cradles have 4 pin, some have 5 pin.
But as you can see, it all goes to positive & negative (red & black) no matter how many pins the cradle has.
The one you showed has Dean's T Plug, but some have Andersons, some have XT60.
I don't know how those two wires are connected to controller, but unless they are soldered to you controller directly, you should be able to separate the controller and battery.
Also what did you mean by "this supplier"? Hulk? or the AliExpress link that I posted?