This article not only cites the words as "wooden shoe" but gives the history of Mairzy Doats as a nursery rhyme, first, and then a song. It also helps explain where some of the other verses came from.

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FRIDAY, FEBRUARY 29, 2008
Mairzy Doats

Mairzy Doats
by Milton Drake, Al Hoffman and Jerry Livingston

Mairzy doats and dozy doats and liddle lamzy divey
A kiddley divey too, wooden shoe?
Mairzy doats and dozy doats and liddle lamzy divey
A kiddley divey too, wooden shoe?

Wow. Both spell-check and grammar-check on Word are lit up like a Christmas tree. Just about every word is flagged. But what the heck: it's Fun-Time Friday! ...

Today's song was a huge hit in the 1940's (more on that in a bit). It was on everyone's lips for years and, I think, still permeates our collective consciousness today. The bouncy little tune plays a perfect counterpoint to the nonsensical syllables. As the singer repeats them over and over, we begin to wonder: Did they swallow too much Pepsodent? Should they switch to Sanka? Are they speaking in tongues? But then the bridge of the song makes it all clear:

If the words sound queer and funny to your ear, a little bit jumbled and jivey,
Sing "Mares eat oats and does eat oats and little lambs eat ivy."

And, armed with that knowledge, we can figure out for ourselves that, "A kid'll eat ivy, too. Wouldn't you?"

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The inspiration for Mairzy Doats came from an English nursery rhyme that begins, "Cowzy tweet and sowzy tweet and liddle sharksy doisters." (Isn't it amazing that, now that you know the "secret" to the song, the whole "Cowzy tweet" line becomes easily readable? Kind of like in The Matrix when those guys could see the whole big picture just by looking at those green letters and numbers.) Milton Drake's four-year old daughter came home from school one day, saying the rhyme. Mr Drake and his buddies, Messrs Hoffman and Livingston, first just set the "cowzy tweet" verse to music, but then decided to write new lyrics instead.

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Mairzy Doats was recorded by "Al Trace and his Silly Symphonists" in 1943. Then, it went all the way to number one with a recording by the "Merry Macs" in 1944. Spike Jones, of course, could not leave well enough alone, and his band's version gilded the lily with their trademark sound effects. The song lifted the spirits of servicemen in World War II. What I find really fascinating is that phrases from the song were used as passwords in the War. Who else but a Yank (or maybe a Brit) would have any idea of the proper response?This article

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That last part, about phrases from Mairzy Doats being used as passwords by the Yanks in WWII is most interesting.