[tyro]

There's insulation on the wires..

You can solder them, just get some solder on your iron and hold it on the wire long enough to tin each wire. It smells bad but it will work. Tin enough of the wire to get it connected to your new plug.

I've fixed a few Sony mdr 7506 the same way.

Edit: had to look up the color of wires in the plug. Green is left (tip of the 3.5mm plug), red is right channel (ring of the plug) and the common is copper or brass colored.

PM me if you need help.