There's an old Irish folksong my father used to sing called "The Crocodile." It had a chorus that began "Jack Was Every Inch the Sailor, five and twenty years a whaler. . ." but as the title implies, he ended up inside a crocodile. Not exactly a fishing song. But perhaps something to serve as filler if you need something?
Wynken, Blynken, and Nod (Eugene Field's poem put to music)
If you find the urge to branch into shellfish, one of the funniest songs I heard in the U.S. Pacific Northwest was "The Geoduck." It had to do with fishermen on a pier.