The repair isn't impossible but it is rather fiddly. I wasn't able to re-use the strain relief and have replaced it with shrink wrap. Here's the colours of the wires for future reference.
I hope Elecraft can choose a different cord in the future so this doesn't happen.
Stephen, VK2BLQ, sent me this picture of a Chinese manufactured mic that came with a CRKits radio. It looks the same and has the same fraying. Perhaps Elecraft gets their mics from the same source?