I don't know anyone who would consider this anything but a glee as sung in the glee clubs by middle class gentlemen in the early nineteenth century. I don't know of any versions that could be construed as even remotely bawdy or risque. In verse 3 'They all began to mate' simply means 'pair off' and references to kissing in some areas might have been seen as off-colour at the height of Victorian prudishness but certainly not in the early nineteenth century among the gentlemen of the glee clubs and supper rooms where they were performed.

I have a sheet music version from the 1830s and broadsides from about 1820 but I doubt it is much older than this although it could be late 18thc. Just about all of the well-known early 19thc printers like Marshall, Pitts, Catnach, Kendrew, Walker printed it but it doesn't turn up in the 18thc garlands.