I would think that mining these early reviews in Gramophone and Musical Times might turn up the goods for you.

Here's an interesting article that's not a review, but about performing shanties, that came up when I Googled on "gramophone sea shanties": FOLK-SONGS OF THE SEA, Shanties on the Gramophone By LLEWELYN C. LLOYD -- Gramophone March 1927. It suffers a bit from OCR errors... I think I'll copy and post this to a separate thread.

O.k., getting earlier: in the August 1926 issue, under "Gramophone Societies' Reports" --

THE BIRMINGHAM GRAMOPHONE SOCIETY.--Tuesday, June 29th, at Ebenezer Chapel board room, Steelhouse Lane. The programme was entirely devoted to records sent by the Parlophone, Vocalion, and Pathh companies. ... A set of two ten-inch Parlophone records of Kenneth Ellis and chorus in several of the sea shanties now so highly popular, were much appreciated...

http://www.gramophone.net/Issue/Page/August%201926/33/793222/Gramophone+Societies+Reports

~ Becky in Long Beach