If you use Windows Vista/Server2k8 or newer you could use mklink to create a symbolic link to the folder containing your application and start the application out of the "symblic linked folder" and then at the update create a new folder, e.g. "AppV2" and change the SymLink to that folder, so the next time the user restarts the application he starts it out of the new folder without noticing.
Renaming open files is ALWAYS a bad choice!
But in general I would think of a better deployment strategy anyway, because if you need to use such "hacks" it is always a messy situation. I don't know your application, but maybee ClickOnce would be a point to start, because you can configure it to check for updates on every start...
