Here's what I remember of the song:

Little Willie the spider wouldn't get out of bed.
He lay the whole morning and scratched on his head.
He had so many legs that it gave him the blues.
All he did the whole morning was put on his shoes.

He woke up one morning when it was still dark
And tied all his shoes on just for a lark.
He ran down the stairs with a smile on his face
And fell with a CRASH when he tripped on a lace.

So my little friends here's a lesson for you,
Don't grumble each time that you put on your shoes.

I remember the tune very well and have sung it once in a while all these years.