The song is way older than any of the above info. There is a 17th century broadside printed in London and the ships were sailing from London which they would have been at that time. Here are some facts re the Scottish version. You can put two and two together if you want.

The Scottish versions all refer to whaling out of Peterhead and Aberdeen c1819.

Peter Buchan, the great ballad fabricator, had his printing press first in Peterhead and then in Aberdeen around this time. He is thought to have written 'Bonny Lass of Fyvie-o' based on the English broadside ballad 'Pretty Peggy of Derby'. Several of the Scottified ballads in his mss are taken straight from English broadsides. As far as I know 'BSTD' does not survive as a Buchan broadside but then rather mysteriously very few of PB's broadsides have survived.

I don't think BSTD is a late piece. I think the Scottish version was made just after the events it describes. There simply was no-one collecting this type of folk song in Scotland until Greig and Duncan came along.