I think this problem can be solved simply and solely by the 
usage of a local web server. 
Don't panic, it's easy to install either on a single PC or 
within a local network.
Look at the www.apachefriends.org homepage, get the "light" 
version, unzip it and then you can administer your walled 
garden.
The users always works with the "true" sitenames -
but you can redirect the allowed (mirrored) sites to the 
place where they reside on your disk.
All http error pages that might appear at forbidden links
(i.e. "not found") you can replace with your own coded or 
modificated ones (which may include a redirect to previous 
page). 
In the same way it's also possible to allow (per 
definition) a true web traffic to a limited  list of sites