Every speaker transducer is inherently balanced. You can run it with a so called 'balanced' (technically differential) signal. You just need a separate 'minus' wire for each headphone cup. Normally left and right are connected somewhere in the wiring to save on wire strands. Normal cable has only three strands, because the ground wire from left and right is shared. You need to identify where it is and circumvent this part. For example if it's a Y-split cable, then the connection must be in the cable. So you replace the cable with a 'balanced' one and you're good to go. If your headphone has a socket, but only on one side, then the connection is in the cup and you need to open it and modify it so that you can solder a cable with separate 'minus' strands. The socket may for example have only three pins in which case you need to get rid of it