Further disassembly is not required and if you're confident in your ability to solder the battery wiring quickly I'd actually recommend against further disassembly. As you can see, I tore the flex cable connecting the LED Indicator section of the flex to the charging pins inside the top half of the housing.

Desolder the Black, White, and Red wires that connect the battery to the LED Indicator flex cable. Then clean the pads with some desoldering braid (gently so that you don't remove insulator from the flex) and reverse the process with your new battery. Black to B-, White to N, Red to B+.

Once your new battery is installed make sure to test it by attaching a power source to the USB-C Charging Port at the bottom of the housing. Watch for the LED Indicator status light to pulse Orange.