There are wire strippers that will go to that size wire. It might take a metric size.
You don't want to hear my suggestion but I'm putting it out there anyway... You should pull new stranded, flexible wire. Strip and tin the ends before pulling. Use the existing wire to pull in the new. A little bit of slack inside the arm tube is not a problem.
Once you have the cartridge end finished you can trim and finish the table end.
Edit: I looked, it can be had for a couple of dollars a foot, $20 for the four wires, color coded and the end clips already soldered on. Cheap to get it right.