Sorcha....
I never heard anybody use the term 'muff' to mean 'Fanny' or 'behind'... but in the US, I have heard it to mean .. 'Beaver' or 'snatch'.. hence the term 'muff-diver' which I think speaks for itself. Using the term 'Muff' in that manner seems to be most common in the Northeast.

When a friend of mine called somebody a 'Muff-diver' as a deragotory term in the company of a bunch of folks from the Western states, they had no clue as to its meaning. Explaining it to them wasn't easy - we kept busting out in laughter. I have heard some bawdy versions of Muffin Man that refer to 'Muff-Diving' but I haven't a good memory for lyrics to bawdy parody songs. I'll ask around. I wasn't going to mention it at all because I didn't think we were going in that direction.

The whole stink about that film "Do You Know The Muffin man' was quite real and heated. The film was made and shown at a time when many of these literal Witch-Hunts were ongoing. Since that time, many of the accused have been exonerated. The film is touted by SRA experts (Satanic Ritual Abuse) as a 'realistic' portrayal of SRA and as a result, many people in the US now believe that the song has sinister origins which is why this entire thread began.