Here's an attempt at summarizing the recordings chronologically so far. Sorry for any mistakes.

1905

--Minster Singers:

(Victor 61145) "The Capstan Bar"
(61146) "Blow, My Bully Boys" and "Sally Brown"
(61147) "Whisky Johnny," and "Shenandoah"
(61148) "Rio Grande" and "Blow the Man Down"

From John Bradford and Arthur Fagge _Old Sea Chanties_ (1904)

1917

--Henry Burr and Albert Campbell:

(Victor 18327) "Shenandoah"

From ??

pre 1925[July]

--John Goss and the Cathedral Singers

(His Master's Voice, B.1999) "Rio Grande", "Billy Boy," "Shenandoah"

From Terry, _The Shanty Book_ (1921).

(HMV B.2018) "Can't you dance the polka?" Arranged E. J. Moeran & "A-Roving," Arranged by Cecil J. Sharp, from _English Folk-Chanteys_ (1914)?

pre 1926[Aug]

--Kenneth Ellis and chorus

(Parlophone E.5583) "Amsterdam (also known as A-roving)", Shenandoah"
(Parlophone E.5584) "The Drunken Sailor," "Santy Anna," "Lowlands Away"
(E.5585) "Rio Grande," "Reuben Ranzo," "Blow the man down," "Johnny come down to Hilo."

*Probably* from Terry and/or Sharp

pre 1927[March]        

--John Buckley and chorus

(Vocalion X. 9786) "Tom's gone to Hilo," "Billy Boy," "Rio Grande," "Blow the man down"
(Vocalion X.9787) "Shenandoah," "Johnny come down to Hilo," "A long time ago," "Fire down below"

--Robert Carr and the Seafarers

(V.F.1159) "Billy Boy," "Blow the man down," and "Shenandoah"
(V.F.1163) "Rio Grande," and "Johnny come down to Hilo"
(Edison Bell V.F.1164) "The Drunken Sailor", "Whisky Johnny"

--John Thorne and male trio

(Aco G.15870) "The Shantyman's Song," "Can't you dance the polka?", "The Drunken Sailor," "Johnny come down to Hilo"
(G.15824) "Haul away Joe," "Rio Grande," "Shenandoah," and "Billy Boy"

1928[Jan]

--Raymond Newell and Chorus

(Columbia 4689) "Johnny Come Down to Hilo", "The Hog's Eye Man", "We're All Bound to Go"

From Terry's The Shanty Book.
***

From this batch, the following items of repertoire appeared (w/ number of frequency):

A-Roving (2)
Billy Boy (4)
Blow the Man Down (4)
Blow, Boys, Blow
Can't you dance the polka? (2)
Capstan Bar
Drunken Sailor (3)
Fire down below
Haul away Joe
Hog's Eye Man
Johnny come down to Hilo (5)
Long time ago
Lowlands Away
Reuben Ranzo
Rio Grande (6)
Sally Brown
Santy Anna
Shantyman's Song (Huckleberry Hunting)
Shenandoah (7)
Tom's gone to Hilo
We're All Bound to Go (Heave Away My Johnnies)
Whiskey Johnny (2)