Thin short wire to wire soldering

In the ppt file, you may see 4 thin wires at the pipe output. The wires can not be pulled out anymore. I want them to be connected to 4 pins head socket (green circle below) via wires on the right. The tricky thing is to solder 4 wires to 4 wires. The wires are insulated outside currently and should not be electrically connected with each others.