> I like to clear out the Explorer 'New' context menu
> (open Explorer, right click and go 'New'). This
> includes the 'WinHTTrack Project' entry. Everytime
> you run WinHTTrack however, it adds this entry back

This is a function of Explorer, not httrack.  

If you open httack using the desktop toolbar instead of the desktop/start menu
- then explorer won't have an entry in the most recent/new lists.