Thanks, MMario, it's nice to not have to re-invent the wheel. They seem to have settled on "rigadoo" being a corruption of "rigadoon", a country dance, and made a pretty good argument for that meaning. But I'm in one of those moods, so I'll stir things up a bit. The other suggested meanings were a walking stick or a pack. Let's go one better. I sense that the rigadoo comprised the walking stick and the pack and the sack--in other words, all his gear as an assemblage. Here's my reasoning:

"You sing for your supper and there's nothing left to do, but to go around the corner with your old rigadoo." Singing is mentioned, but not dancing. Now there's nothing left to do (i.e., you're done singing--and if you'd been dancing that's done too) so you head out, carrying your stuff.

"Hello, Mr. Beggarman, and how do you do, with your rags and your tags and your old rigadoo?" She's enumerating his possessions--it would be very odd to include a dance in this question.

"So now you've heard the story of my old rigadoo" We've heard about some of his things and about his lifestyle, but no mention of dancing.

So I contend that "rigadoo" as a dance does not make much sense in the contexts where it is used. It makes sense to me if it means his gear as a whole. I am now prepared for the onslaught from those who see it differently and/or know better than I (G).