It's er-lye in the mornin' and according to Joanna Colcord, SONGS OF AMERICAN SAILORMEN, © 1938, pp. 53-57, "Blow the Man Down" was primarily associated with the Atlantic Black Ball Line (not to be confused with the Australian Black Ball Line):

It should be noted that in those days, "blow" meant "knock."

C. Fox Smith has an extended discussion of "Blow the Man Down" in A BOOK OF SHANTIES, © 1927, p. 49, but no direct reference to the meaning of "blow." However, in one of the versions she includes of the shanty the meaning of the word is unambiguous:

So they gave me three months all in Liverpool town --
To me way-ay, blow the man down!
For fighting a p'leeceman and blowing him down --
Give me some time to blow the man down!

Incidently, there is more evidence in Colcord that she and C. Fox Smith were well aware of each other; they do have a record of correspondence in the Colcord archives. Colcord quotes large passages from Smith's SAILOR-TOWN DAYS with regard to background for "Blow the Man Down."

It's possible that the big East Indies ships of the early 19th century also used bosun's pipes for ordering the crews to work; they emulated the Royal Navy practices in many ways.

Cheerily,
Charley Noble