I recall a full parody titled "My Grandfather's Hat." It dated, I believe, to the 1920s or 30s.

All I recall of it is the first line:

"My Grandfather's hat was too big for his head ..."

I don't think I have any written version, but I will scout around.

Bob

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From https://mudcat.org/Detail.CFM?messages__Message_ID=1555163:

(Campaign of 1888) His Grandfather's Hat.txt
AIR -- 'Grandfather's Clock'

His grandfather's hat is too big for his head,
But Ben tries it on just the same
It fits him too quick which has oft times been said
With regard to his grandfather's fame
It was bought long ago, and it made a pretty show
In that jolly 'hard cider campaign'
But it don't fit even a little bit on Benjamin Harrison's brain


[Benjamin's Harrison's grandfather, 'Tippecanoe' won the presidency in 1840 as whig.]