Alternatively, you could have a simple change in filmmaking patterns. No Hollywood. Have the US movie industry grow up on the East Coast. Until the 1900s, there was plenty of adventure lit about the sea. one reason why Hollywood produced so many westerns was that they were reasonably cheap to make in the surrounding countryside and reflected local heritage. A New-York-based industry might just naturally gravitate towards seaboard and harbour scenes, tropical jungles (Georgis and the Carolinas) and harsh arctic environments (Maine). The next generation grows up with the idea that American manhood was forged in the crucible of the fo'c'sle and grew to greatness facing down the cannibals of Fiji and the vicious Russian patrollers of Kamchatka.
Well the American film industry moved west for several reasons, amongst them was that it allowed them to work outside the Motion Pictures Patents Company (AKA Edison Trust) which basically allowed Thomas Edison and friends to hold a monopoly in most of American filmmaking.
Ultimately the Trust was declared a monopoly and an illegal restraint on trade but by then most "independent" filmmakers had moved to Hollywood. As you said, for Hollywood filmmakers making westerns was cheap because of climate, scenery, etc. But if the Trust never goes into effect then most filmmaker stay in New York, others like Griffith (one of the main Hollywood founders) would probably stay in the south.
Thus the American film industry would not be centralized, allowing the existence of cinema with a wider range of genres and styles.
After that you only need a moderately successful "Whaler" film by an independent north eastern studio. Some larger studio digs the idea and releases a big ass blockbuster sometime after 1927 (that is the first academy awards). The movie wins many academy awards. And a whaling craze begins in America.
The whaling movie offers, like the western, a frontier setting between civilization and the wild. It also offers themes of camaraderie (the men in the boat) and romance (the women waiting on shore).
As you said the next generation grows thinking that this is how American manhood was achieved.
The pattern in filmmaking then goes more or less like this:
After WWII occupied Japan catches the trend. They being big whalers start making some whaling movies. Furthermore most of their Samurai films borrow heavily from Whaler films in terms of themes and structure.
Ultimately by the 1950s the craze has died down. The Whaler/Sailor film does not disappear altogether (the Western did not in OTL) but it gets toned down. No more big transoceanic epics but smaller films focussing on the home aspect of whaling. "What really happens with the women who stay home?" "What are the real consequences of living in the sea for so long?" and themes like this. Some times the "Whaling Operas" take place in the west were there are no whales. But these "Horse Operas" play very much like their seafaring counterparts. Some European studio catches the trend and a Euro-whaling movie is released with moderate success.
But in the 1960s Italian and Spanish filmmaker revive the Whaling/Sailor film. They make them violent, manly, and realistic. Very different from the epic American films of the 20s and 30s or the melodramatic versions of the 50s. When these filmmakers pair up with American and other international stars to produce Whaler/Sailor films. They become an international success. Because these films are very cheaply made but so attractive every major studio form America and Europe begins to test the waters. Even British studios, which always stayed away from the western for several reasons, are free to tap into the Whaler movie.
This new craze dies by the 1980s as SciFi creates whaling operas in space. But in the 1990s nostalgia wins out. Some director master of pastiche blends the classical American "Whaling Operas", the European "Spaghetti Whales", and Japanese Whaling and Samurai films. Such films gain cult following and ultimately become mainstream.
In the 2000s a TV show is released. This show sets the Whaler not in its typical late 1800s early 1900s setting. But in a distant and magical past when sea monsters were actually hunted. The TV show is a flop but a spin off movie is released with relative success and cult following.
The Whaler movie will Survive
Film Examples:
Early Whaler: "The Great Whaling Adventure"
Award Winning Classical Epic Whaler: "Salvaje"
1950s Whaler Melodrama: "Paul"
Japanese Whaler: "大きく白いクジラ"
Spaghetti Whaler: "Once Upon a Time in the Northwest"
American Pastiche 1990s: "Once Upon a Time in La Patagonia"
2000s TV Show and Spin off: "Clipper" & "Tranquility"
(Did I just summarize the history of Westerns and replace Western for Whaler? Yes, but I think it sounds OK)