Knick Knacks is one of the terms for Knacker bones which probably go back to before speech was invented, certainly well before 1900. I don't normally indulge in these flights of fancy, but as someone has already mentioned the rhythmic qualities of the chorus here goes:-
Knick-knack, pat and whack, rattle on yer bones, might have been a more apt original.
We sing a similar song in Yorkshire called Old John Braddleum/ Old Jack Braddler which has a different tune, but recently I came across a version to the same tune as 'This Old Man'.
The form is something like:-
Number one, number one, now the fun has just begun,
With a rum pum paddle-um, Owd joe braddleum,
Jolly country lads are we.