Hopefully the fuse blew or you didn't turn the unit on after the wire got cut. I've cut 2 'ducer cables in the past, one was able to be repaired because the fuse blew and protected the head unit, the other didn't have a fuse for some reason and it blew out the head unit and was beyond repair.
I don't think you need to worry too much about the shielding, as long as the cut isn't right next to other electronics or wiring you should be just fine. The one I was able to repair I just twisted the braided wire together and soldered all the small wires. That was two years ago and haven't had any problems doing it this way. Just make sure its a couple feet away from anything that has electicity in it.
Like W2S said it won't cost you anything to try fixing it yourself just make sure you have the proper size fuse before turning everything back on.