The first time I ever heard of Nellie McKay was when she played "The Dog Song" on piano on the Letterman show. I bought her "Get Away from Me" album the next week. It's a great album, even though she wasn't playing the uke then.
I think that the punches during the verses are just individual notes played in octaves on the original, and not chords. But it didn't sound good on the uke that way. And the chord sheet I found on Ultimate Guitar Tab treated these as chords. So I played them as the chords that I think are implied by those notes. I made several changes from the Ultimate Guitar Tab version.