How about this? It has been a while and memory fades but I believe this is pretty much the version we used to hear on the radio:

WILLY CLAUS

Santa Claus once caught a cold the night of Christmas Eve.
Though he planned to make his trip, he felt too sick to leave.
Suddenly he heard the bells a-jingling on his sleigh.
He looked out in time to see his outfit pull away.
Willy Claus, Willy Claus, little son of Santa Claus,
Hitched the reindeers to the sleigh.
Willy Claus, Willy Claus, little son of Santa Claus,
Cracked the whip and drove away.
"Giddyup, giddyup!" Willy hollered. "Giddyup!"
Driving southward in the night.
Sing-l-ing, ting-l-ing, with the bells a-jing-l-ing,
Willy soon was out of sight.

Mama Claus came rushing in and breathlessly she said:
"I just looked in Willy's room and Willy's not in bed."
"Dear, oh dear!" cried Santa Claus. "I think he's run away.
He had on his new green suit and drove off in my sleigh."
Willy Claus, Willy Claus, little son of Santa Claus,
Had a job to do that night.
Willy Claus, Willy Claus, little son of Santa Claus,
Went down chimneys left and right.
Bicycles, choo-choo trains, lots of dolls and aeroplanes,
He left toys for everyone: water guns, cowboy hats,
Little dogs and pussycats, like Santa would have done.

Christmas morn, the sleigh flew home across the snow-white plains.
Mom and Santa saw at once that no one held the reins.
Out they ran to search the sleigh and when they looked in back,
Guess who they found sound asleep upon the empty sack:
Willy Claus, Willy Claus, little son of Santa Claus.
Two more gifts were all he had in his arms, in his arms.
They nestled in his arms. One sad mom, and one sad dad,
Santa Claus, Mama Claus smiled on little Willy Claus,
Then they picked up their son.
Willy Claus, Willy Claus, little son of Santa Claus,
Whispered, "God bless everyone."