As noted above, there are two issues. First, determine the integrity of the damaged wires. If just chafed but otherwise structurally sound, a good repair with some fusion type electrical tape and then rewrapping the harness might be all you need. If a wiggle test indicates an actual break in the wires, or close visual inspection indicates any broken strands, a better approach would be as Twolanerider suggested, cutting out the damaged area and splicing in some new wire, then rewrapping the harness. Then send the radio off for proper repair. Those who have just had Harley replace those radio's with more of the same have been reporting repeat failures since 2006, so I agree with the others that you will be better off sending it to Iron Cross and having it fixed right.
Btw, those fairing and speaker brackets have been improved since 2006, so you might want to just replace all four pieces while you've got everything torn apart. I did the bandaid repairs on a couple ocassions on my '05, only to have the bracket break again in a different spot, but I've had no further problem since installing all new brackets.
Jerry