Some nine copies in the Bodleian of the one mentioned in the Ballad Index; for the record here it is.

SAUCY SAILOR BOY

1
Oh, come my own one, come my fond one
Come my dearest unto me,
Will you wed with a poor sailor lad,
That's just returned from sea?
2
O you are dirty, love, you are ragged, love,
And smell so strong of tar,
So begone you saucy sailor boy,
So begone you, Jack Tar,
3
If I'm dirty, love, if I'm ragged, love,
And smell so strong of tar,
I have got silver in my pocket, love,
And gold in bright store.
4
As soon as she heard him say so,
Down on her bended knees she fell,
She says, I will love my Henry,
I will love my jolly sailor well.
5
Do you think I am foolish, love?
Do you think I am mad?
For to wed a poor country girl,
When there's a fortune to be had.
5
So I'll cross the briny ocean,
Where the meadows are so green,
And since you have refused my offer, love,
Some other girl shall wear the ring.
6
I am frolicsome, I am easy,
Good-tempered and free,
And I don't care a single pin, my boys,
What the world says of me.

Firth c.13(240), Bodleian Collection, H. Such, London, c. 1863-1885.

This seems to me to be a song for teasing, a parlor song for a couple who know nothing of the sea.
I will check some of the others for variant lyrics.