Hi Paul
I'm not sure that you can have a document that's not associated with a template, but I can think of two possible workarounds:
1. Copy the template from your network to your local machine, then re-attach the document to the local version. (I'm currently on a Mac, but the process would be the same: Save the template to the 'My templates' (or similar) folder. Then go through Tools, Templates and Add-ins, Attach (or whatever the corresponding commands are in your version of Word) and attach to the local version.
2. Attach the document to an existing template on your local machine, e.g. the Normal template. Make sure not to check the 'Automatically update document styles' box though.
Hope this helps.
Steve