Here's some more information that I located on another site regarding the repair process that another individual performed:
Reattaching the Transducer’s Signal Wires (SR-60)
Method (Skippy): A voice coil wire broke underneath the diaphragm of my SR60, so I peeled off the diaphragm, and extendend the wire to repair the driver. The transducer consists of the diaphragm, the coil, the magnet assembly, and the big plastic cup part. The coil is glued to the diaphragm, and the magnet assembly is plastic cup. the magnet assembly consists of a circular magnet in the center, and a metal ring (more like a cup actually) surrounding the magnet. the voice coil sits inside the gap in between the magnet and the ring.
The diaphragm is stuck on to the big plastic cup part using glue. This glue isn’t too strong, around the same adhesiveness as scotch tape. I used a pin to separate the diaphragm from the plastic cup – moving very slowly and very carefully.
I slowly peeled the diaphragm off, exposing the voice coil. Carefully, I unwound a loop of wire from the coil. Then I replaced the diaphragm back onto the transducer. The glue residue was still sticky enough to hold the diaphragm without using any extra glue. That part was hard, but it gets harder.
I couldn’t dissolve the enamel coating on the wire. Usually I scrape the stuff off, but the Grado wire is so thin and fragile that any scraping would rip the wire to shreds. Unfortunately, scraping the enamel was the only method I had left. I shredded the wire many times and almost had to remove the diaphragm again to unwind another loop, but I was finally able to scrape off the enamel without breaking the wires.
Soldering those wires is hard because they’re so thin and fragile. I couldn’t even hold them with tweezers without snapping them. I ended up using the tip of the soldering iron to control the wire. It actually worked very well.
Note: the wires that connect to the transducer are uninsulated. When the cord moves around the uninsulated wires brush up against each other, causing clicking sounds. A little electrical tape fixes this easily.