So far, I haven't been able to locate the web site that describes how you can alter the behavior of the New Word Document right-click (context) command in Windows Explorer. (Frankly, I don't even remember if the workaround can be used for any versions of Word and Windows, so it may not apply to your system anyway.)
For easy access to the template of your choice, you can add a shortcut on the desktop. See
http://support.microsoft.com/kb/210565/en-us/.