Disconnect the charger. Let it sit for half an hour or a day so the caps discharge.

Open the case. Insert a flathead screwdriver and pry until you hear a loud click. Then lever the two plastic cover out.

Rotate the DC side (because the wires are joined in the middle) and slide the entire thing out.

Solder the wire. A AWG 20 is good enough. You don't want it to be too thin because it might need to carry some current, but it don't need to be too thick.

Put everything back. The plastic covers might be loose so you can apply a little bit of glue. hot glue is preferred as it don't generate fumes. otherwise one or two drops of epoxy will do. Or just use straps, tapes or whatever.