My battery had swelled to the point that the screen was being pushed out of the case. I had previously replaced my screen successfully, so I decided to try this seemingly simple (and, it is relatively simple) repair.
I followed all the steps and everything went smoothly until I found that the old battery just was not willing to come off the sticky tape which holds it to the back of the case. I pried at all the recommended places and even broke one of the pry tools, trying to raise it even a little. So, I re read the other posts and tried a small crafter's heat gun to soften the glue. This worked well and the battery began to let go. Finally, I decided to twist the pry tool at the top of the battery. I tried to keep within the 2mm limit but, when the glue finally let go, I realized that I had, indeed, torn the volume control cable almost all the way through.
At work, I use a microscope and work with very small parts, so I took a look. The volume control cable is basically a flat wide foil, sandwiched between two flat layers of plastic tape and is stuck to the back floor of the phone. Using the back side of the point of a scalpel blade, I cut some of the insulation off the flat copper foil and was able to deftly overlap the two ends and make contact. After reassembly everything seems to be working fine. I consider myself very lucky.
Do not risk cutting that cable. One of the other posts mentioned slipping a loop of dental floss under around the battery to lift it safely. This may be a better solution. The heat gun actually did wonders to soften the sticky stuff. It's not magic. If I had known that what's holding the battery in place is no more than double stick tape, I would have been more confident.
You can do this. Just know that that cable is really there and it cuts like butter.