It should be 'wringing', but that means twisting her hands around each other in despair (as in "She fell in to despair/a-wringing of her hands and a tearing of her hair/'Since my Johnny's gone and left me, no man alive I'll take/But all my days on Claudy's banks/I'll wander for his sake') not his neck! Entwining hands on his neck I take to have been done affectionately! Of course, you are free to wewrite the song to make it more tragic and violent! The words remind me of another song:
Don't talk of leaving me here, dearest William,
Don't talk of leaving me here by the shore
For youo know that our parting in sorrow will grieve me
Stay at home, dearest William,
To the seas do not go

(I think one recording is by Cathal McConnell, Boys of the Lough)
I'm reminded also of High Germany (in database) and also of those songs in which the woman DO@ES dress up and go to sea. And there's an @parting category in the database if you particularly like farewell songs. You'll also find there's a [false young man] for every [fair young maid]. For slaying the false young man, don't forget Child no. 4 (False Sir John, The Outlandish Knight, etc. in the DT)