"Cape Horn theme" is a construct of Hugill's mind that he's bringing to the table, as he evidently felt it was a neat and/or compelling way to organize.

1. J. C. Colcord "Songs of American Sailormen" (1938)

A bully ship and a bully crew,
   - Doo-da, Doo-da!
A bully mate and a captain too,
   - Doo-da, Doo-da-day!

[THIS IS A GENERIC VERSE]

       *2*
Round Cape Horn in the month of May,
Round Cape Horn in the month of May

[THIS IS CAPE HORN]

       *3*
We came to a land where the cocktail flows,
We came to a land where the cocktail flows

[GENERIC]

       *4*
Came to a river and I couldn't get across,
Jumped on a slaver* and I thought he was hoss

[THIS IS FROM "POOR OLD MAN," A MINSTREL VERSE]


3. F. P. Harlow "The Making Of A Sailor" (1928)

Oh, New York's race course is nine miles long.
   - To me hoodah! To me hoodah!
Oh, New York's race course is nine miles long.
   - To me hoodah! hoodah day!

[THIS IS "DE CAMPTOWN LADIES"]

       *2*
A bully ship and a bully crew,
A bully mate and a skipper too.

[GENERIC]

       *3*
Oh, New York's race track, where we stood,
We bet on all they said was good.

[DE CAMPTOWN LADIES (RACE TRACK)]

       *4*
Our watch, our shoes and every rag,
But lost our money on a bob-tail nag.

[DE CAMPTOWN LADIES]

       *5*
Our money all gone we shipped to go
Around Cape Horn, where strong wids blow.

[CAPE HORN]

       *6*
We're bound for Californi-o;
For gold and banks of sacramento.
[GOLD RUSH - COULD RELATE TO CAPE HORN]


5. W. M. Doerflinger "Shantymen and Shantyboys! (1951)

It Was in the year eighteen hundred and forty nine,
   - With me hoodah, and me hoodah,
It Was in the year eighteen hundred and forty nine,
   - A with me hoodah, hoodah ay!

[GOLD RUSH]

       *2*
Were Going around the Horn and home again!
Were Going around the Horn and home again!
[CAPE HORN]

We sailed away one day in May,
And when we came out into the Bay,
[GOLD RUSH, MAYBE CAPE HORN]

       *4*
We got into Bay and then did sail!
We got into Bay and then did sail!
[REMAINING VERSES COULD BE CAPE HORN, BUT ALSO GENERIC]

So the only one of these that arguably sticks to "Cape Horn" related stuff is the last one.

Hugill sorted the verses into "versions" by presenting each as if they were exclusively devoted to a single theme. As someone who has sung chanties many times, and never sings them the same way twice, I find this hard to believe. It's just not how the brain works, of an improvising musician. You're thinking of "Sacremento" from the chorus, so maybe you singing about Frisco Bay. Then you're thinking of "De Camptown Ladies" (the original melody) so you steal a line from that. Then the minstrel quality of "De Camptown Ladies" sets your mind on other minstrel-style verses, so you go into "Poor Old Man." Then you fill time with a generic verse like "Was you every down Mobile Bay." Then, "Bay" puts your mind on another rhyme you've heard, "90 days is damn good pay"..."I thought I heard my captain say"..."A dollar a day won't pay my way", and on and on.
That's why, myself, I didn't feel it was necessary to sing every solo verse Hugill put down on the page. I consider them as the broader "language of chanties" and a pool from which to draw. Which verses I come up with don't change the chanty to one version or another. I see the true variations in terms of melodies and chorus lyrics.

I think it's worth learning/studying the verses of Hugill to acquire that "language." But I discard Hugill's analysis because I don't think he was equipped to analyze and I'm frustrated by how he clouded his life experiences and his reading and presented that as research. I also cloud my experiences with what I've read for performing. "Anything goes" when singing. Research is different :)