When creating a new store, I am going to use the same categories/products.
What I want to be able to do is to create specific URLs for that new country store.... I am presuming the front end 'product description' - Category names' - product and CMS page URLs are all independently controlled from within the Admin area and not affected by what the Main store settings may be?
In the admin under Catalog -> Manage Products and Manage Categories there is a selector on the left side of the page for "Choose store view".
You can choose the Website/Store that you want to manage and override all of the default settings for categories and products.
To have different urls just edit the url key for them.