You _could_ fix them without a soldering iron or solder, but it wouldn't be the easiest thing in the world to do. Often you can simply cut a bit of the plastic insulation from a wire, then twist 2 wires together and it'll work just fine. I don't know if the wire from the marshmellows are like this, but I doubt it
What is more likely is that those wires are enamel-coated. This means that every little strand of wire is not only protected by the plastic insulation, but by clear enamel (think clear nail polish) as well. Normally with a soldering iron you can melt it fairly quickly, and then solder or twist the wires as normal. If you still want to try it, I would suggest this:
Snipe the connector off the end, and a connector from other headphones that you want to use. Take off an inch or so of plastic insulation from both pieces and try twisting the correct colours together. If after that it doesn't work, try using a lighter (very carefully) to burn off the enamel. It may take a bit, but it _should_ work. Once you've done that, twist the correct colour wires together, tape each colour up seperately (so the wires don't touch each other) and see if they work.
Hope this helps!
They only cost me 10$ but I just want to fix these. i have a couple of headphones at home that I could use the end connector off of.
