I spoke too soon. The recording I linked to above is indeed an instrumental, but the same collection also contains 2 vocal recordings, from which I transcribed
this: (There is still a word or two in line 2 that I can't get.)

SHALL I HAVE IT BOBBED OR SHINGLED
By Bert Lee (1881-1946) and R. P. (Robert Patrick) Weston, (1878-1936)

1. Sweet Suzy Simpson had such lovely hair; it reached down to her waist.
Till friends sweetly told her that around Mayfair having hair was ...(?) taste.
"Bobbed or shingled it must be, dear," said they, "if you wish to wed."
Till in black despair in the fatal chair in the hairdresser's shop she said:

CHORUS: "Shall I have it bobbed or shingled? Shall I have it shingled or bobbed?
Sister Cissy says, 'Oh, have it shorn short, Sue,
Shingled, shorn and shaven like the swell set do.'
Shall I have it shingled shorter?" said Suzy as she sighed and sobbed.
"Sister Cissy said she'd sooner see it short and shingled,
But both my brothers Bert and Bobby say it's better bobbed."

2. Inside Woolworth's store this afternoon, a clerk sat sad and blue.
Her manager happened by that way and said "What's wrong with you?
If you find that your work's too hard, I will help you with your task."
Then the maiden sighed and softly cried, "Here's a question I'd like to ask: CHORUS

3. Inside a butcher shop in Golders Green, just after closing time,
A cat got her tail in the sausage machine and was cut off in her prime.
She ran out with her tail ripped off and swanked it to the cats with pride,
And the tabs and toms put their to's and froms in the sausage machine and cried: CHORUS

4. Lady Godiva on a snow-white mare once rode through Coventry,
And she was wearing all her lovely hair. Oh, it reached down to her knee.
Peeping Tom at his windowpane exclaimed when he saw the sight:
"Oh, your hair's all wrong, 'cause it's much too long," and Godiva replied, "You're right.... CHORUS

[The above is a composite of 2 recordings: one by Ernest le Messurier in 1925
has verses 1, 3, and 4; another by Al Plunkett in 1926 has verses 1, 2, and 3.]