Yup thats correct. A lot more verses thought.

Here's the first 2.

This old man, he played one;
He played knick-knack on my thumb.
With a knick-knack, paddy whack,
Give a dog a bone;
This old man came rolling home.

This old man, he played two;
He played knick-knack on my shoe.
With a knick-knack, paddy whack,
Give a dog a bone;
This old man came rolling home.