Thanks for those latest comments and information. At this point a chronology of the Molly Malone version of 'Cockles and Mussels' set in Dublin might be in order:

1871 First sighting of lyrics of two verses of Molly version in 'gagbook' of the clown Thomas Lawrence, no author's name.

1876 Earliest discovered words and music of Molly version, published in Boston, Mass, in the students' songbook 'Carmina Collegensia', no author's name.

1876 Sheet music edition of version starring Jim the Mussel Man and set in London, author J B Geoghegan, air and lyrics different but chorus very similar to Molly version.

1880-1900 (or earlier?) Dundee Poet's Box edition of lyrics of Molly version, no author's name.

1882 'Ladies Treasury' magazine stated that 'Mr Geoghegan' composed
the Dublin version of the song, but admittedly could have confused it with the London version.

1884 Sheet music edition of the Molly version stating that James Yorkston was the composer and that it was reprinted from 'Musical Treasury' number 35 [about March 1882, not traced], published by Kohler & Sons of Edinburgh. (Yorkston was primarily an arranger with no track record of composing popular songs, and there was at this time in Edinburgh another and 'respectable' James Geoghegan, choirmaster of the Old Greyfriars Kirk, which might have rendered use of J B's name problematic.)

Again, case not at all proven, but J B Geoghegan's name remains in contention for authorship of the classic Molly Malone version of 'Cockles and Mussels'.