The goldfish one (round and round and round) I heard Judy Cook sing as alternate lyrics to Auld Lang Syne, not a hymn, but same funny effect (particularly since that's one song folks can seldom get past the first verse)

Stan Rogers' "Tiny Fish For Japan" "Jeannie C"

"Codfish Ball" - might have come from Shirley Temple - I know it as a jug band piece done by the Smokin' Fez Monkeys

"Good Fish Chowder" on a Deb Cowan album - FUN singalong as she does it.

"Hey Ho Little Fishes" - Bok, Muir Tricket or Cooper & Nelson versions
"Dance to thy Daddy"both lullaby sorts of songs

Archie Fisher's "Final Trawl" - end of the life of a fishing boat.
Jeannie C is one of a slew of fishing boat disaster songs, that are more about the boat than fishing. like" Threescore and Ten" & ""The Bergen" (Jez Lowe)

Joanne in Cleveland, contemplating the concept of fishing in post EPA times.