Hmm, I know the rear subframe is entirely different, not sure about the up-front part. The claw is also different, and of course instrumentation, if you take the instrument package off the Touring tank there's an indentation underneath there as well as mounts for the instrument itself that would look quite unsightly without the instrument package. So even assuming it fits the frame from underneath you'd be left with issues. The instrument cluster is probably not a straight retrofit to the Classic, and the Touring electronics differ somewhat also (for instance, we get turn signal cancellation that the Classics don't). Etc.
So I don't think it would be a simple swap.