I regret to report I have not, though they've been on my list for some years. But the joke sounds, by reputation at least, very much of the sort O'Brian would enjoy.
a 120-ton Spanish galleon that sailed the Peru–Panama trading route during the 16th century. This ship has earned a place in maritime history not only by virtue of being Sir Francis Drake's most famous prize, but also because of her colourful nickname, Cagafuego ("fireshitter")
Okay, but in entire fairness, I did say "any empire would give". If she wasn't actually commissioned under the name as the Merriam-Webster blog suggests, I believe this qualifies as having successfully weaseled out.
Certainly it makes a lot more sense as a nickname! Those have vastly broader range than commissioned names typically do. In any case, I appreciate your effort in finding a more reliable reference, especially one that adds such color and provenance to a swear I grew up around and have favored since earliest childhood.
My family always uses it when talking about the dog going caca. It used to confuse me when I was a kid but we’d say shishi for pee. Family is mixed so it’s not really pidgeon but more just mixed. A Korean friend heard me say shishi once and said they say the same in Korean, which was surprising to learn but like caca it’s probably a fairly universal word
Cacafuego is the name of a much bigger ship that Jack Aubrey captures.
Of course, that's fiction, and the speculation is that POB chose that name as a sort of inside joke.