That's probably reasonably close. There's an undated broadside edition at  Bodleian Library Broadside Ballads which also has a song by Fred Alberts, who was active in the 1870s:

Buttercup Joe

Gwilym Davies will know more about the song than I do (it's still to be found in the wild out there, though mostly deriving from Albert Richardson's famous recording, perhaps) and Billy Weeks will probably know about Harry Garratt. With luck, they'll spot the thread.