He completely freaked out when he heard the squeaks. Cried inconsolably and refused to walk on them while yelling "HENNY! HENNY!" I guess he felt that he was stepping on chickens with every step.
The packaging, website, and the lady who sold me the shoes all said that the squeaks were removable. I could not see a way to do that without damaging the shoes.
So here is our public service message. If you have these shoes, and want them not to squeak, all you have to do is plug the little air outlet hole near the heel. We are currently using a piece of scotch tape for this purpose, but I'm sure caulk, play-doh, silly putty, or any of a multitude of similar substances would work.