Here are several references to "Cheerily Men" from the 1840's. First of all from the MEMIORS OF THE REV. WALTER M. LOWRIE: MISSIONARY TO CHINA, ed. Walter Lowerie, 1849, perhaps talking about 1842. The occasion is the hoisting of guns out of the hold to be mounted.

http://books.google.com/books?id=eotjAAAAMAAJ&pg=PA110&dq=Cheerily,+Men&lr=&cd=139#v=onepage&q=Cheerily%2C%20Men&f=false

A second reference comes from A VISIT TO THE ANTIPODES: WITH SOME REMINISCENCES OF SOJOURN IN AUSTRALIA, by E. Lloyd, "A Squatter", 1846, perhaps referencing events in 1844. The location is Port Adelaide, and the author is reflecting on an abandoned ship and imagining the song "Cheerily men, ho!".

http://books.google.com/books?id=X8MNAAAAQAAJ&pg=PA77&dq=Cheerily,+Men&lr=&cd=138#v=onepage&q=Cheerily%2C%20Men&f=false

The next reference comes from MCDONALD OF OREGON: A TALE OF TWO SHORES, by Eva Emery Dye, 1906. The biography is "based on personal statements and letters of McDonald...", etc. (p. v). The events take place in the harbor of Nagasaki, Japan, in 1849. The song "Cheerily, men, oh!" is mentioned several times in different settings, one of which is a rowing scene. There may be some question about whether this is an historical "reconstruction".

http://books.google.com/books?id=1dUVAAAAYAAJ&pg=PA250&dq=Cheerily,+Men&lr=&cd=99#v=onepage&q=Cheerily%2C%20Men&f=false

And here is a reference to "Haul her away!", from Ezekiel I. Barra's A TALE OF TWO OCEANS, published in 1893, but perhaps referencing 1849.

http://books.google.com/books?id=v6oqQ1CiaGYC&pg=PA11&lpg=PA11&dq=%22Haul+Her+Away%22&source=bl&ots=mdCKZL6pkZ&sig=kQ14HcLcH8QKA