What kind of cable is used to connect the two parts of headphones
If this is the cable that runs between the two earpieces, all you need is two conductors. 

The original cable uses enamelled wire of two different colors. The enamel coating with burn off when you tin the conductors. Simply twist all of the strands of one color together, then hold the twisted wires in a ball of molten solder on your soldering iron tip. 

Be careful not to get one strand of the other color in the twisted bundle - this would result in a short circuit.