Can the iOS 6 setup assistant be re-run a second time without erasing my iPhone?

If I recall correctly - perhaps others can help flesh out any missing details - the setup wizard primarily lets you sign in with / sign up for an Apple ID to use for iCloud, it asks you to agree to the iCloud Terms of Service, and it asks about setting up Location Services.

All of these can be accessed directly through the Settings app at any time. I don't believe you will miss any important functionality by missing the wizard, especially if you were previously using your iPhone with iCloud in iOS5.

Go to Settings > General > Reset > Erase All Content and Settings. After a reboot, you will be on the setup screen.