I wondered if the above song were a parody of this one, but apparently not.

From the sheet music at the UCLA Archive of Popular American Music:

I DON'T WANT TO BE A SOLDIER BOY
Words by George V. Hobart. Music by Karl Hoschna.
M. Witmark & Sons, ©1910.

1. Once I lived in a shop
Where the kids used to stop
Grinning through the window pane,
For the toys are the joys
Of the girls and the boys;
That is why we all are vain.
In the store near the door
Was a doll, oh, so small!
Gee, but I did love that dear!
But my sword and braid
Made her sore afraid,
Till I whispered in her ear:

CHORUS: "Oh, I don't want to be a soldier boy.
I'd get shot as like as not.
I don't want to have a bullet come
And hit me where it hurts an awful lot.
I don't want to be a soldier boy.
I don't want to go and hide.
I'm just longing for my toy store window
With my sweetheart by my side."

2. So I stayed in the shop
Where the kids used to stop,
Wishing for each toy in sight.
On the doll I would call,
And she'd say, ev'ry day:
"Soldier, are you going to fight?"
I'd reply with a sigh:
"Not for mine; I decline.
Reason to you I will tell:
Mister Sherman knew
Just a thing or two
When he said war was awful!