There seem to have been several of these songs where the song is interspersed with sounds.
Inventive singers and reciters could have made up their own variations, as you say was done by your Grandpa.

This one may have contributed.

Little Pigs

Little Pigs lie on the best of straw,
Straw, straw, shan diddle daw,
Little Pigs lie on the best of straw,
Strawm straw, shan diddle daw,
Lillepirluri, my dad was a bonny wee man,
Our little pigs eat the best of potatoes,
Pratees, pratees, shan diddle datoes,
Our little pigs, etc.

The old sow taught the little-un's to grunt,
Grunt, grunt, shan diddle grunt.
The old sow, etc.

Our little pigs make the best of bacon,
Bacon, bacon shan diddle daken,
Our little pigs, etc.

Our old sow's got the hooping cough,
Cough, cough, shan diddle boff,
Our old sow, etc.

Now here's an end to our good song,
Song, song, shan diddle dong,
And here's an end, etc.

Bodleian Collection, Firth c.16(43), c. 1840-1850.