The attached doc has the pinout for that JST connector so the wire color won't matter, just count the pins carefully. I would cut the jumper cable roughly in half, strip the ends of only the wires you need: Audio out , Ground , Audio In , PTT
I would first solder those four to a small PCB such as the ones in this Elegoo kit on Amazon
ELEGOO 32 Pcs Double Sided PCB Board Prototype Kit for DIY Soldering with 5 Sizes Compatible with Arduino Kits
https://m.media-amazon.com/images/I/91MBDISdwhL._SL1500_.jpg
Then you can run out the heavier external wires to whatever connector you will plug into your radio. Be sure to have some sort of strain relief so that the external wires can't be tugged at. If you can't find a way to fasten down the little PCB board somewhere inside the radio, wrap it in electrical tape after you finish testing.
On the heavier wires you should add some Ferrite beads to choke off any RF that might get coupled in.