It's not all that complicated to knock out the pin that secures the barrel and move the barrel to center, then reinstall the pin. That small amount of travel should not require any lathe work or other expensive metal removal.

However, moving a barrel is tricky, and if done wrong you can really do some damage. I would venture the smart thing to do is pack that baby up and send it to S&W for the "tweak". That way you'll know it was properly done, you'll sleep better at night doing it that way!