On the same token, if you cloned me, and he was sitting next to me and I had to choose who would get shot, I'd choose him. He isn't me because I can't access his thoughts. I think identity is tied to physical and temporal location and is in continual flux, so a clone is never me--it never occupies the same points in space and time. The nerve replacement idea is tough, though. Maybe our idea of identity is wrong, artificial, or too limiting.
I wouldn't care, and I'd bet that neither would you.
Think of it this way - were you ever shocked by the teleporters in Star Trek? After all, this is precisely what they did: make a copy of someone, then dissolve the old copy.