Here is my list:

Hauling & Halyard Chanteys

"My Dollar And A Half A Day"/"Lowlands" c
"Walk Me Along, Johnny" / "General Taylor" c
"Mr. Stormalong"
"Yankee John, Stormalong"
"Stormy Along, John"
"'Way Stormalong John"
"Stormalong, Lads, Stormy"
"A Long Time Ago" (a) / "In Frisco Bay" [h]
"Goodbye, My Love, Goodbye"
"Roll The Old Chariot"
"Roll The Cotton Down"
"Roll The Woodpile Down"
"Sally Brown" (b) (c) (d) c
"Rolling Home By The Silvery Moon" (later)
"Knock A Man Down"
"Huckleberry Picking" / "We'll Ranzo Ray"
"Hilo, Johnny Brown"
"Shallow Brown"
"The Gal With the Blue Dress On"
"John, Come Tell Us As We Haul Away"/ "Mobile Bay" c
"Gimme My Banjo" [h]
"Run, Let The Bullgine Run"
"Walk Along My Rosie"
"Coal Black Rosie"
"Bunch O Roses"
"Way, Me Susiana" [h] c
"Round The Corner Sally"
"Sister Susan"/"Shinbone Al"
"Walkalong, Miss Susiana Brown"
"Dixie Land" / "Sing A Song, Blow-Along O!"
"Bully In The Alley"
"Fire Maringo" c
"Blow Boys, Blow"
"One More Day"
"Yankee Dollar"
"Poor Old Man" / "Dead Horse"
"John Cherokee" (Colcord)
"Hilo Come Down Below" (Bullen)
"The Bully Boat"/"Ranzo Ray" (a) (Sharp)
"Little Sally Racket" (Laura Smith)
"Cheerily, Men"
"Tommy's Gone Away" (c Sharp)
"Whisky Johnny"
"Billy Riley"
"Hello, Somebody"
"High O, Come Roll Me Over"
"Where Am I to Go, M'Johnnies"
"Roll, Boys, Roll"
"Ranzo Ray" (c)
"Hello Somebody"
"Can't Ye Hilo?"
"John Kanaka"
"Haul 'er Away" (a) [h]
"Haul Away, Boys, Haul Away"
"Walkalong, My Rosie"
"Do Let Me Lone, Susan"
"Sing Sally O" (b)
"Essequibo River"
"Dan Dan"
"Hilonday" L. Smith
"Pay Me the Money Down" [h]
"Walkalong You Sally Brown"
"Hilo Boys Hilo"
"Tiddy High O"
"Heave Away Boys, Heave Away" (b) c
"Sister Susan (Shinbone Al)" [h]
"Eki Dumah" [h]
"Miss Lucy Loo" [h]
"Heave Away Boys, Heave Away" (a) c
"Tommy's on the Tops'l yard"
"Haul 'er Away" (b)/ "Nancy Fanana"
"Good Morning Ladies All" (b) c (Olmstead)
"Won't Ye Go My Way?" [h]
"Tom's Gone To Hilo"
"Hanging Johnny"
"So Early In The Morning" (a) / "Bottle O"
"So Handy, Me Boys"
"Golden Chariot" (Doerflinger)
"Shanandore" (Bullen) & "Shanadar" (Sharp)
"Leave Her, Johnny"
"Seraphina"
"Baltimore"
"Across The Western Ocean"
"Hurrah, Sing Fare Ye Well" [h]
"Hoorah For The Blackball Line"
"Lower The Boat Down" (Colcord)
"A Hundred Years Ago" (a) (b)/ "'Tis Time For Us To Go"

"Hieland Laddie" c [stamp 'n go]
"Rise Me Up from Down Below" [stamp 'n go]
"Drunken Sailor" [stamp 'n go/hand over hand]
"Johnny, Come Along" [stamp 'n go]
"John Dameray" / "Johnny Come Down The Backstay" [stamp 'n go]
"Boney" / "John Francois"   [short haul & halyards]
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A number of these chanteys were used for multiple purposes.
c = cotton stowing/screwing
[h] = "hauling" (Hugill)
(a) (b) (c) = different versions in Hugill '61