Not that is can be expressed in a text-only medium, but what's the tune?

And is it essentially a five-line stanza?

If never we return again
No more shall we tarry
We'll leave a song on the Western Wind
Sing it again for Mr Finn
And haul away for Barry!

My memory of most shanties (not my specialty, for sure) is that the short second line would typically be mirrored in the fourth line, so I tried cutting your last line into two short lines instead.

I almost think you could drop the "Mr. Finn" part and just leave the "haul away for Barry" in its place:

If never we return again
No more shall we tarry
We'll leave a song on the Western Wind
And haul away for Barry!

Your mileage may vary.

I may have more comments on the lyric in a while.

Bob Clayton