I guess the flexible flat cable has three conductors: minus, plus, and NTC. The NTC is probably on the BMS board, connected to the minus and NTC conductors. Probably, the NTC is a 10 kΩ one.
That is, there are two wires between the battery proper and the BMS board, and three wires between the BMS board and the battery connector.
I assume that the right tool is a soldering iron, not a spot welder. You need a spot welder for round cells, but not for Lipo cells.