You can use URL rewrites to edit the displayed URL, but without changing your actual wordpress setup all your internal links will still point to the structure assigned in your permalinks settings.
The most straightforward way to do this would be by using a custom post type. With CPTs you can set up a whole different structure for your posts and get as customized or as standard as you want with how wordpress handles it, both internally and externally. You can even make custom taxonomies (post categories is an example of a taxonomy) and associate it only with that CPT.
You can do this manually by editing your functions.php file (good tutorial here) or use a plugin like this one to do the heavy lifting for you.
Here’s the codex for registering CPTs
I’ve recently gotten pretty deep into custom post types, use role creation and management and such. It’s really powerful and will save you a lot of hassle with URL rewrites.