The charging port on the headphone melted

@salmanirfan my first point of interest would be why it melted. There may be more damage than just the port. Post a couple of well focused and large images of the damage, the board etc. with your Question.

If it is "just" the connector, you could replace it by soldering a new connector in its place. USB -C ports are a bit more involved due to the pins on the underside. You will need a good rework station and experience to replace it. To disassemble it use something like this video and/or this one It might be a slightly different model but it should still work for your Bose as well.

There will be a challenge to find the replacement connector. You may have to find one that fits, by scouring Digikey.com or Mouser.com I would recommend that you replace the complete charging board. You would need something like this Example only.