Maybe a little (a lot?) late, but searching for a way to do the very same, finally found the way.
The trick is to remove a registry key:
HKEY_LOCAL_MACHINE\SystemFileAssociations\.jpg\Shell\setdesktopwallpaper
That's for jpg files, but repeat searching the same route with different file extensions and you can delete the context menu option for each one individually. The changes should take effect immediately, without reboot or logoff.