I have a repo (origin) on a USB key that I cloned on my hard drive (local). I moved \"origin\" to a NAS and successfully tested cloning it from here.
I would like to
You can
git remote set-url origin new.git.url/here
(see git help remote) or you can edit .git/config and change the URLs there. You're not in any danger of losing history unless you do something very silly (and if you're worried, just make a copy of your repo, since your repo is your history.)
git help remote
.git/config