See if there is a way you can align the wire to wrap in a circular position on the inside and around the circles that wrap around your ears, where you hear the music from.
If you can't do this properly, a professional may need special tools to get inside the headphones in order to align the wire properly. I wouldn't try opening the device yourself, because these devices, believe it or not, are more fragile than even the biggest cassette decks, for instance.
I tried to repair my 8 track player myself because it was making a loud muffling noise. I was successful, but I ended up tightening a screw so much that if the same problem happened in the future, I wouldn't be able to get in with the tools and knowledge and experience I have.
Portable players are more fragile because their parts are, well, just small and very delicate. Although it is possible to repair these items yourself, most people would not advise it.
Although you have to be very careful when repairing portable devices, audio and video repair shops often charge less to repair portable devices since they don't need to use as many tools to repair them. Often, with careful measures, for professionals, it is a quick, easy, and simple fix.
I would call up local audio repair shops in your area and see the prices to diagnose and repair them (some will just tell you the diagnosing price unless you actually go to the store and show them your malfunctioning item). Then see which shops offer the best repairing deals, and go to the shop with the best deal.
As a rule of thumb, if it costs more to repair than you paid for your device or than it would cost to get a similar device, just buy a new device and donate or throw away your old device.
I hope this helped.
experience with home and portable music players and accessories for nearly four years