Here's my version FWIW.

As I was a-walking down Paradise Street
Tibby* way, hay, blow the man down
A flash-looking packet I chanced for to meet.
Gimme some time to blow the man down

(2nd and 4th refrain lines omitted below.)

She hove alongside me and hailed me so free.
"Me hold is empty, I'm ready for sea".

(Chorus after every second verse)
Blow the man down, bullies, blow the man down
Tibby way, hay, blow the man down
Blow him right back into Liverpool Town
Gimme some time to blow the man down.

What country she come from I can't tell you which
But by her appearance I'd say she was Dutch.

Her flag wore its colours. Her masthead was low.
She was round in the quarters and bluff in the bow†.

Well I hailed her in English and hailed her in Dutch.
But she says "Me young feller, you're talking too much."

So I hailed her in French and the signal she knew.
She backed her main tops'l and for me hove to.

Well I gave her me hawser and took her in tow.
And yardarm to yardarm together we go.

She lowered her mains'l, maintops'l and all
(Let) her lily-white hand on me reef tackle fall

Well I lifted her hatches, found plenty of room
So into her cabin I stowed my jib-boom.

I entered her holds, both for'd and aft†
And into her harbour I sailed my trim craft.

But at length Jack says "Well it's time to give o'er"
"For betwixt wind and water you've run me ashore."

"Me shot locker's empty, me powder's all spent."
"I can't fire a shot for it's choked at the vent."

Here's health to the girl with the long curly locks.
Here's health to the girl as brought Jack on the rocks.

Here's health to the doctor who cured all his pain.
Now he's squared his main yard and he's cruising again.

* I once heard Stan Hugill state forcefully that it is "tibby", not "to me".
† These lines can be accompanied by gestures.