Make the external drive internal then make the internal drive external.Move things around.
The way I said isn't right anyways.Why not just start using your external instead?
Is the external hard drive a portable hard-drive?
You can't make Windows recognize a different drive as the primary without reformatting.
If you just want to run your programs off an external drive you can simply redirect each shortcut to the new file location after reinstalling the game on the external drive. Some games and systems (Steam?) don't really give you an option though. You can alter where your browser sends saved files as well.
If the external drive was a usb drive wouldn't that make it a lot slower?