In the US, fanny is a slang term for buttocks. It isn't rude in any way, it's the kind of thing your grandmother might say. "I fell right on my fanny in the middle of the store!" "Or maybe "You'll get your fanny warmed up good if you keep on sassing me back!"
In the UK, I understand that it means the female private parts.
So no, Fanny is far beyond its shelf life.
Before you criticize a man, walk a mile in his shoes. That way, when you criticize him, you're a mile away and you have his shoes!
Steve Martin