In a 1909 book, "Heart Songs", which is a 502-page American collection of "popular" songs, is a song simply titled "English Chanty". Its chorus lines are multiple repetitions of "Cheerly, Men", but it's different from the commonly known "Cheerly Man" in structure, melody, and lyrics. At Joe Offer's request, I'm posting the lyrics here. If I can learn how, I'll add the melody.

ENGLISH CHANTY

Come shipmates and brothers,
        Ho yo! Cheerly, men,
Haul all together
        Ho yo! Cheerly, men,
Help one another,
        Ho yo! Cheerly, men,
        O hauley, ho yo, Cheerly, men!

[the indented parts are the chorus, with the other verses following the same pattern]

The wind it blows hard,
Each tar knows his card,
We'll soon man the yards,

Come, loose ev'ry sail,
We'll soon face the gale,
Stout hearts which ne'er fail,

Our hearts they are light,
Each eye it seems bright,
We bid you goodnight,
        O hauley, ho yo, Cheerly, men!