Try talking to some of the folky Whitby residents. People such as Derek Elliott would know what belongs to the town.
You could also ask permission from people who have written songs more recently.
Richard Grainger wrote one called Whitby Whaler - he can be tried via the web sites for the Captain Cook/Shanty festivals.
Bill Sables, who is a mudcatter, although I'm not sure how often he looks in these days, wrote one called Whitby Fisherman (to an old American Hymn tune).
Quack!
Geoff the Duck.