Well, there are 2 registry keys related to Explorer Extension:
HKEY_CLASSES_ROOT\*\shellex\ContextMenuHandlers\avast
HKEY_CLASSES_ROOT\Folder\shellex\ContextMenuHandlers\avast
The first is for files, the other one for folders.
However, if these registry items got corrupted, then the "Scan..." item wouldn't appear at all in the menu.
Are you familiar with tools like
File Monitor and
Registry Monitor? I'm not very optimistic, but maybe they could tell us something more about what happens at the moment when you select the "Scan..." item from the menu.