I seem to be late to this thread. I got this song from "The Burl Ives Folio of Australian Folk Songs"*, which gave it as "blue-bellied joe". However this just seems to be a variant of "bare-bellied". In either case the point was that a sheep without much wool on its belly would be easier and therefore quicker to shear, and speed was a point of pride among the shearers.

The dictionaries seem to agree that the "ringer" was the fastest shearer in the shed, but can't agree on the meaning of "snagger". However one definition is the slowest shearer, and this would make sense in the context of the song - the fastest shearer is beaten by the slowest, who had grabbed a blue-bellied joe and was able to complete the job with one less blow (a sweeping cut) of the shears.

* "collected and arranged by Dr Percy Jones". I doubt Burl Ives had much to do with it beyond allowing his name and photo on the front cover.