Here is my summary of what I think I'm being told:
One way to do it (safest, in my mind): Re-name, and save project to an external hard drive. Then go to my internal HD and delete everything I don't want (virtually all the old related files, as I see it). Sound right?
Another way is to just rename it, and Save As in the computer,
then delete everything that had been generated (my saves, or Auto Save). If This is correct, I think I would prefer the ext. HD best.