I've traveled the wide world over, and many things I saw, but
a speaking-tube on a whaling ship I never saw before.

No, really. I've tromped all over vintage vessels, some restored,
some reconstructed, and some really awful. Now, on the powered
vessels (both steam and vintage internal-combustion) there
inevitably have been speaking tubes running from bridge to
engine room, and often a few other places (such as to the
wardroom or charthouse). This even has been the case on light-ships.

But never, no nay not once, have I ever seen such a thing on a
sailing vessel of any kind. From coasters to whalers to packet
ships, I've not seen hide nor hair of such a communications
device. Nor any sign that any such thing was ever there. Amongst
all that original hardware, from binnacles to bits and even
basins, nary a speaking tube in sight.

Now this is purely anecdotal, and lacking in 'documentary evidence.'

But it convinces me that 'Blow the Man Down' hadn't a thing to do
with such a acoustical contrivance.

It should be noted that the speaking tube was not the primary means
of communication twixt engine room and bridge--- that came via the
telegraph. The speaking-tube would have been resorted to when
that didn't work, and would have served as the conduit of choice
words, coaching, and exhortations, and excuses. Presumably it
would have functioned fairly well in the age of steam, which is
relatively silent save perhaps for the sounds made by the blowers
on the boilers, and a lot less well in the presence of internal
combustion engines.

As to other references to being blown down, I give you 'The Ebenezer'
verse one:

"I shipped on board the Ebenezer
Every day was scrub and grease her
Send us aloft to scrape her down
And if we growled they'd blow us down"

Other parts of the "Ebenezer" use language which implies
origins similar in time and place to 'Blow the Man Down.'

Context makes it pretty clear to me.

The watch below was called up with a clatter on the
scuttle and "take your hands from your cocks and pull on
your socks."