Here's the version I learned in elementary music class abt 1956:

DOCTOR IRON BEARD

Oh, I'm the Dr. Iron Beard,
Tolly winkle toll de-ay
A man the well have never feared,
Tolly winkle toll de-ay
But many ill ones come to me,
the blind to walk, the lame to see;
I conquer every misery,
Tolly winkle toll de-ay.

A lady had an aching tooth,
Tolly winkle toll de-ay
She came to me and then, forsooth,
Tolly winkle toll de-ay
I wound the tooth with ball and string,
then gave the ball a mighty fling;
Her cure was most astonishing!
Tolly winkle toll de-ay.

There was a man in Boston town,
Tolly winkle toll de-ay
Who creaked whenever he sat down,
Tolly winkle toll de-ay
I gave him bitter Cal-o-mel,
a mile away they heard him yell!
Tolly winkle toll de-ay.

So come to Dr. Iron Beard,
Tolly winkle toll de-ay
You'll wish you never had appeared,
Tolly winkle toll de-ay
My patients come through snow and rain
and leave without an ache or pain,
but never do they come again,
Tolly winkle toll de-ay.

As a professional Storyteller, I present as "Dr. Iron Beard." That's my 'handle.' When I present to children, I often sing this song. I never knew here were other words.