I've just figured out the answer myself. It actually hit me while I was typing the question, but I still think it is worth posting for further reference.
The solution I've found is to create an empty folder and name it
Network Connections.{7007acc7-3202-11d1-aad2-00805fc1270e}
I've found the list of CLSIDs available for this trick here.
But let's go further. I hate having icons on my desktop and I've found the way to put this to the start menu top level:
Create the folder (named as shown above) wherever on the hard drive.
Create (I've created it on the desktop and removed it at the end) a shortcut to explorer.exe
with the folder full name as the parameter like this:
explorer.exe c:\Quasifolders\Network Connections.{7007acc7-3202-11d1-aad2-00805fc1270e}
Change the icon and the name.
Drag it into the Start menu.
Delete it from the Desktop.
UPDATE:
I've found out that you don't even need to create an Explorer shortcut. Just put the avatar folder wherever you want (as I've said, it is needed to remain there) and drag it into the Start menu.
That looks interesting, but could you just script your actions using netsh or Powershell? Might be more efficient in the long run especially if they're often repeated commands. – trpt4him – 2012-12-14T13:53:48.017
Oh, maybe later, @trpt4him. The technology is actually here and not changed since I've been using it in Windows 98 :-) – Ivan – 2012-12-14T14:30:43.383