Though it doesn't mention Christmas, several web sites classify this as a Christmas song.

Lyrics copied from http://www.geocities.com/Hollywood/Academy/3225/Country/Marion_Worth/Shake_Me_I_Rattle.txt

SHAKE ME I RATTLE (SQUEEZE ME I CRY)
(Hal Hackady and Charles Naylor)

I was passing by a toy shop on the corner of the square
Where a little girl was looking in the window there.
She was looking at a dolly in a dress of rosy red,
And around the pretty dolly hung a little sign that said:
    Shake me, I rattle. Squeeze me, I cry.
As I stood there beside her, I could hear her sigh:
    Shake me, I rattle. Squeeze me, I cry.
    Please take me home and love me.

I recalled another toy shop on a square so long ago
Where I saw a little dolly that I wanted so.
I remembered, I remembered how I longed to make it mine,
And around that other dolly hung another little sign:
    Shake me, I rattle. Squeeze me, I cry.
I had counted my pennies, just a penny shy.
    Shake me, I rattle. Squeeze me, I cry.
    Please take me home and love me.

It was late and snow was falling as the shoppers hurried by,
Past the girlie at the window with her little head held high.
They were closing up the toy shop as I hurried through the door,
Just in time to buy the dolly that her heart was longing for.
    Shake me, I rattle. Squeeze me, I cry.
And I gave her the dolly that we both had longed to buy.
    Shake me, I rattle. Squeeze me, I cry.
    Please take me home and love me.

[Recorded by the Lennon Sisters in 1957, Marion Worth in 1963 (Peaked at # 42 on the Billboard Pop chart and # 14 on the C&W chart) , Cristy Lane, and Lisa Brokop.]