Get another working headphone jack. You can cannibalise a cable you don't need or just buy one on Amazon.

Get a soldering iron, many cities also have stuff like makerspaces or something like that where you can borrow one.

Also, maybe get some heat shrink tubing.

Snip off the end of the cable, solder on the new jack, done.

Even if you were to buy a new soldering iron off of Amazon this entire thing is doable for like $20. Also, soldering really isn't hard even if you have never done it before.