Being as blunt as possible, would individuals in the English kingdom have viewed this as a dick joke? He earned the nickname from his poor military acumen, but I was wondering if any evidence supported the idea that he was called this for non-military reasons as well.
While I can't speak directly on the nickname, I can say that John was known to be sexually voracious, often sleeping with his Barons' wives, although he had no heirs. In 1204 he charged Joan de Neville 200 chickens for the right to sleep with her own husband Hugh (a member of the royal court) for a night, rather than with him.
So on balance I would argue that no the nickname does not have a sexual undertone. It certainly fits with the other jibes aimed at him, Lackland and 'Reynardie', or fox - like.
Daniel Crook 'Hugh de Neville' in Oxford Dictionary of National Biography