What we had was 0.3mm diameter wire, which is already insulated. On this type of wire you can remove the insulation coating where you want contact by boiling it off with a soldering iron

The old wires will indicate the length you need. They seem rather long and you can make the replacement shorter. But don't get too short. You need some slack for reassembly.

Solder both wires to the PCB contacts and fit the other end through the hole near the center axis. If you have two same colored wires, mark one of them before you put them through the hole, so you know which is plus and which is ground.