Probably older than the 1820s. Charles Dickens lets a drunken cook recite part of the lyrics in Two Dinner Failures (1855) and Cecil Sharp, who collected the song in London and in Bristol, 'obviously a bagpipe tune', used on board as a work song.
John Goss & the Cathedral Male Voice Quartet [as What Shall We Do With The Drunken Sailor]
David Guion [folk arrangement as What To Do With A Drunken Sailor; he also wrote Ol' Paint and contributed to Home On The Range, Turkey In The Straw and The Arkansas Traveler]
Captain Richard Maitland [Lomax recording as What Shall We Do With A Drunken Sailor]
Richard Dyer-Bennett [idem]
Mordy Bauman [on Songs Of American Sailor Men]
Ferre Grignard [hit B, NL & Fr]
Babe [hit NL]
David Thomas [as What Do We Do With A Drunken Sailor on Rogue's Gallery]
The chorus reminds Irish trad. ballad Oró Sé Do Bheatha Abhaile (see there).