'Most of the shanties before the 19th century are of British origin...'

Perhaps someone would like to name one!

Phil, of course you are correct. There is a lot of fiction and fabrication attached to what is now perceived as chanty/chantey/shanty.
However we can't escape from the fact that there was a recognisable type of worksong, sung mainly in English, aboard Anglo-American vessels from the 1830s onwards that appears to have at least its main origin in the Gulf ports and Carribean. There were definite embryonic rowing songs that can be related to these noted down from c1810 onwards, but the main impetus can be traced from cotton screwing aboard ships in dock to chequerboard crews and then universally. These can be easily linked up. What relationship any of these have to other traditions of worksongs at sea is a very grey area if any link at all.

Seeing as we have these different spellings, here's a suggestion, we use 'shanty' to describe all of the fabrication that went on post 1880 and 'chanty' to describe all of the noted down material prior to that.