You’re right, the kind of cable often used is not easy to solder. This makes it hard to solder a broken cable together again, or to replace a broken / bent plug. So best replace the entire cable and its plug — it’s still an inexpensive part.

You’ll need to solder it to the contacts inside the can, but that’s quite straightforward.

In case the internal cable that goes from one can to the other breaks, you can replace it with any bit of audio cable so you can use one that’s easy to solder.