I need to assign some tags to my posts (for external use), but I don't want them showing anywhere that tags are listed. Can someone tell me how to do this?
The best way is not to do this. Use a custom taxonomy instead.
I echo @toscho's suggestion. You can setup a taxonomy via your functions.php (use the reference he gave you) file or by using a plugin like Ultimate Taxonomy Manager.
A custom taxonomy will let you organize your posts as you'd like, without worry about interference with the standard post tags.