Grab the right-angled stereo plug to pigtail cable and measure up the length you'll need. If you cut it too short, you can always extend by splicing with a longer wire.
You'll want to remove about 10mm of insultation from the audio cable. Use wire cutters or a hobby knife to strip the wire. Carefuly bundle the stranded wire and twist it together to make a uniform wire - this is the ground connection.
Secure the audio cable to third-helping hands. Apply solder to the ground connection. Trim one of the insulated wires (red or white, doesn't matter these are the 'left' and 'right' channels). We only need one channel and the ground connection. Strip and tin the remaining wire.
Trim off about half of the tinned ground connection (it's too long). Prep a new piece of AWG30 silicone-coated stranded wire by measuring, cutting and stripping. Solder it to the ground connection.
Slide a piece of shrink tubing over the ground connection and apply heat to secure the connection. Cut the ground wire to match the length of the channel wire and tin the tip.