I found various sources for some of your lyrics by searching on "grandma chews them in her sleep." Some of these were just jumprope rhymes (in fact there's one of those in the Mudcat archives already); several were songs. Here's one from this Canadian Boy Scouts site. No tune was posted, but perhaps you remember that. If not, a thorough Internet search should get you lots of info:

GRANDPA'S WHISKERS

I have a dear old Grandpa
His hair is turning grey,
He has a pair of whiskers,
They're always in the way !

Chorus:

Oh they're always in the way,
The cows eat them for hay.
They cover the dirt,
On Grandpa's shirt,
They're always in the way.

I have a dear old uncle
He owns a Ford machine
He uses Grandpa's whiskers
To strain the gasoline !

Chorus

I have a dear old Grandma
And when she goes to sleep,
She chews on Grandpa's whiskers,
And thinks they're shredded wheat !

Chorus

Every Monday morning,
We gather in a group,
To watch Grandpa's whiskers
A dangling in the soup.