Perhaps this will shed some light on the topic, via
languagehat.com : THROUGH A TIN HORN.
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The appearance of the word āshitā in print was restricted in the past. So I think it makes sense, as a start, to gather evidence by looking for variants of the phrase in the major text databases.
Here are some variant phrases that appeared in newspapers and periodicals beginning in the 1880s:
like butter through a tin horn
like water through a tin horn
like mud through a tin-horn
Here is an example of ālike butter through a tin hornā in 1887. A boat was grounded on a bar in a river. Eventually, a strategy was found to move the boat forward past the bar.
Cite: 1887 October 09, Kansas City Times, Science in Navigation,
[Acknowledgement to Mobile Register], Page 19, Column 4, Kansas City, Missouri. (GenealogyBank)
[Begin excerpt]
Then the rope was tied to a tree on the bank above and the old Carrier went over that bar like butter through a tin horn.
[End excerpt]
In the domain of sports, the phrase āwater through a tin hornā was used with quotation marks in 1897. It was used to describe a runner easily penetrating the defense of the opposing team and scoring a touchdown.
Cite: 1897 December 26, Oregonian, āFought In Deep Mud: Multnomah Wins Christmas Football Game, 10-6ā³, Page 8, Quote in Column 2. Portland, Oregon. (Genealogybank)
[Begin excerpt]
Wilbur was given the ball, and, with fine interference, plunged through Multnomahās line like āwater through a tin hornā and scored Portlandās only touchdown.
[End excerpt]
The phrase ālike mud through a tin-hornā was used in quotes in 1906. The word āmudā was sometimes used as a euphemism for āshitā in periodicals. So the phrase ālike shit through a tin-hornā may have been used by a pilot in the following excerpt.
Cite: 1906 December, The Rudder, Volume 17, Number 12, A Fast Trip Down the Hudson by Walter M. Bieling, Quote Page 735, The Rudder Publishing Company, New York. (Google Books full view)
The Rudder