Well, I believe you can do it as you said detaching/attaching db. So, I would stop a service, detach db, copy .mdf, .ldf, attach db and run the service. This way you don't have to restart sql service.
Thanks for your thoughts on this.
I performed a standard detach / attach of the cva database and this worked fine.
The tempDB was also located on the C drive. I ran an Alter Database script to move the tempDB file location and restarted the SQL service.
Of note, the home page for our DC RUM (application health status) did not show up any applications or statistics after the SQL restart. Had to wait 15 mins for this to reappear. So don't panic if you do not see status information immediately after doing a DB move.