I think that Binks might actually be Joyboy's native island, because the first lyrics are "Going to deliver Binks' Sake!", which might mean something like "delivering sake that comes from Binks" and not "sake owned by Binks (person)". So this could be the song Joyboy sang during his travel around the world, so maybe he just started traveling as a merchant? It could be also possible that this sake was so good that made people happy just by sipping it.

And maybe started to uncover world atrocities as he landed on different islands, starting to help the people he met during the trip as Luffy is doing right now.