I didn't find a SHANGHAI NELL, but I did find SHANGHAI LIL:
Copied from http://harrywarren.org/songs/0455.htm

SHANGHAI LIL
Words, Al Dubin. Music, Harry Warren. 1933.
Written for: Footlight Parade (1933)
Performer: James Cagney, Ruby Keeler & Studio Chorus

SHEET MUSIC VERSION:

VERSE 1: Temples reaching to the stars, international bazaars,
Chummy little Chinese ladies, drinking at those dinky bars;
Balmy breezes from the sea, blossoms in the cherry tree,
Ev'rything is so familiar, but where, oh, where is she;

CHORUS: I've covered ev'ry little highway,
And I've been climbing ev'ry hill,
I've been lookin' high and I've been lookin' low,
Lookin' for my Shanghai Lil.
The stars that hang high over Shanghai
Bring back the mem'ry of a thrill,
I've been lookin' high and I've been lookin' low,
Lookin' for my Shanghai Lil.
I learned to love 'er,
The little devil was just a butterfly;
But you'd discover
Something on the level shining in her eye.
Oh, I've been tryin' to forget 'er,
But what's the use, I never will,
I'll be lookin' high and I'll be lookin' low,
Till I find my Shanghai Lil.

VERSE 2 (FROM BRITISH SHEET MUSIC):
Anxiously I cast an eye on each street throughout Shanghai,
Plenty Oriental ladies beckon as they pass me by;
But my mind just can't erase one outstanding lovely face,
So, until the day I find out, I'll never leave this place. [CHORUS]


MOVIE VERSION:

INTRODUCTION:

(WOMAN 1, SPOKEN:) Looking for your Shanghai Lil?
(CHINESE MAN, SPOKEN:) No, she ain't your Shanghai Lil.
(WOMAN 2, SPOKEN:) Don't give him flowers,
He'll just take your flowers
Straight to Shanghai Lil.
(BARTENDER, SPOKEN:) No, I ain't seen Shanghai Lil.

VERSE (HALF-SUNG):

(SAILOR:) Hello, Bill, you old galoot,
Where'd you get that monkey suit?
(JAMES CAGNEY:) Don't tell anyone you saw me
Or I'll rap you in the snoot.
(SAILOR:) Hey, you jumped ship, now what's your game?
(CAGNEY:) Oh, just lookin' for a dame.
(SAILOR:) Staying here, you're takin' chances.
(CAGNEY:) Yeah, well I'll stay just the same.

CHORUS 1:

(CAGNEY, SUNG:) I've covered ev'ry little highway
And I've been climbin' ev'ry hill.
I've been lookin' high
And I've been lookin' low,
Lookin' for my Shanghai Lil.
The stars that hang high over Shanghai
Bring back the mem'ry of a thrill.
I've been lookin' high
And I've been lookin' low,
Lookin' for my Shanghai Lil.
I learned to love her,
The little devil
Was just (LAUGHS) a butterfly;
But you discover
Something on the level
Shining in her eye.
Oh, I've been tryin' to forget her,
But what's the use, I never will.
I'll be lookin' high
And I'll be lookin' low,
Lookin' for my Shanghai Lil.

(CAGNEY, SPOKEN:) I've got to have another brandy!

CHORUS 2 (PEOPLE AT BAR, ALL SINGING):

(WOMAN 1:) He's shaking like he's got a chill.
(WOMAN 2:)I know what it takes
To cure him of the shakes;
(MAN 1, SPOKEN:) Ah, what he wants is Shanghai Lil;
(MAN 2, SUNG:) Oh, she's a fascinatin' heathen,
(WOMAN 3, SPOKEN:) But say, she ain't been through the mill.
(MAN 3, SPOKEN:) Since she met that gob,
She's acting like a snob.
(WOMAN 4, SPOKEN:) Say, who the heck is Shanghai Lil?
(WOMAN 5, SPOKEN:) That Chinee devil!
(WOMAN 6, SPOKEN:) No, she's on the level,
(WOMAN 6, SUNG:) She can't hurt you and me.
(WOMAN 7, SUNG:) That oriental
Dame is detrimental
To our industry.
(WOMAN 8, SPOKEN:) You said it!
(MAN 4, SUNG (British accent):) I offered 'er a 'ouse in London…
(MAN 5, SUNG:) And I a château in the ville.
(MAN 6, SUNG:) She said she won't be mine
For all of Palestine, oy!
(WOMAN 9:) They all go for Shanghai Lil.

INTERLUDE:

INSTRUMENTAL

(SAILOR, SPOKEN:) Come on, let's drink to Lil;
He's lookin' for her still,
Drink her down to Shanghai Lil.
(ALL, SPOKEN:) Hey!

CHORUS 3:

(ALL, SUNG:) Here's to the gal who loves a sailor,
Here's hopin' that she always will;
(SAILOR:) She's ev'ry sailor's pal,
She's anybody's gal!
(ALL, SUNG:) Drink her down, to Shanghai Lil.

INTERLUDE (FIGHT):

INSTRUMENTAL

PARTIAL CHORUS 4:

(SAILORs, SUNG:) He can knock 'em down
And he can lay 'em low,
Fighting for his…
(CAGNEY, SPOKEN:) Shanghai Lil!

CHORUS 5:

(KEELER, SUNG:) I miss you very much a long time,
I think that you no love me still.
(CAGNEY, SUNG:) I've been lookin' high
And I've been lookin' low,
Lookin' for you, Shanghai Lil.
(KEELER, SUNG:) I think you go with other sweetheart,
And very many tears I spill.
(SAILORS:) He's been lookin' high
And he's been lookin' low,
Lookin' for you, Shanghai Lil.
(KEELER, SPOKEN:) I got new lover.
(CAGNEY, SPOKEN:) You little devil,
(CAGNEY, SUNG:) You're just a butterfly!
(KEELER:) I like new lover.
(CAGNEY:) You're still on the level?
You can't kid this guy.
(KEELER:) I pray to Buddha in the joss-house
And Buddha, he bring back my Bill.
(SAILORS:) He's been lookin' high
And he's been lookin' low,
Lookin' for you, Shanghai Lil.

INTERLUDE (KEELER & CAGNEY TAP-DANCE, MILITARY DRILLS
AND FORMATIONS):

INSTRUMENTAL

PARTIAL CHORUS 6:

(KEELER:) Oh please, you take me
On great big steamboat
With you across the sea?
(CAGNEY:) I'd like to take you,
But that great big steamboat
Don't belong to me.

CHORUS 7:

(CHORUS:) The stars that hang high over Shanghai
Bring back the memory of a thrill.
I've been lookin' high
And I've been lookin' low,
Lookin' for my Shanghai Lil.
I learned to love her,
The little devil
Was just a butterfly;
But you discover
Something on the level
Shining in her eye.
Oh, I've been tryin' to forget her,
But what's the use, I never will.
I've been lookin' high
And I'll be lookin' low,
Till I find my Shanghai Lil.