Here's my transcription, partially from that youtube video and partially from a fragment recording I have where she sings "we" instead of "I" and adds a chorus. Thanks for your help!

Said the sirens to the sailor
What makes you think we want your sorry ass washed up here on our beach?
We’re so out of your reach
Just goes to show there’s nothing ever comes for free
You say you got our number
It was scribbled on some drunken sailor’s dank and hairy palm
Well you got it all wrong
Just goes to show you can’t believe everything that you read
We just come to this beach to sing

Chorus:
And when we sing, we sing the blue ocean
We sing the whitecaps, we sing the waves
We sing the winds, we sing the stories
We sing the breaking of the day

Said the sirens to the sailor
We’ve yet to meet the man the likes of which we take with open arms
The topman from the yards
No washed up salt come all this way to cop a feel
You must have heard the stories
The blind man says we girls all do it just for sport
That’s myth and no more
Just goes to show you can’t believe everything that you read
We just come to this beach to sing

Chorus

Said the sirens to the sailor
Somewhere along the line I’d like to think that we could get some flash
Could settle some hash
Could see our names and lights our reputation clean (???)
We’d like to think we’d settle
For just a bit of honest ink writ large inside the Times
No doggerel rhymes
Just goes to show you can’t believe everything that you read
We just come to this beach to sing