'2. he uses the sheepskin as a ploy to threaten her into cooperation'
In the Child versions it doesn't specify whether he actually puts it into action or not, but in many of the later versions from oral tradition he goes whickety whack on her back (i.e., the sheepskin). In some even later versions the animal skin motif is dropped altogether.

The song is an item from our past, our heritage, and as much as we nowadays abhor the content, it is a dangerous thing to deny the past, even for 7-year-olds. How early should we start teaching the Holocaust for instance? The song could certainly be used as a starting point for the discussion of our violent/mysogenist past, or present even!

As the thread is about 'The Wee Cooper of Fife' I think children would just accept it for what it is as most of us did when we sang it, a jolly little song. I think even a 7-year-old can understand it is an old song and a piece of fiction. If we were to slim down the school repertoire of all references to violence etc. we would end up with a repertoire of those incipid 18th century pastoral pieces and bore them to death.