As a child (1976-ish) we had a 78 speed record of this song, sounded like a radio show host from the 50's singing it, with a Gomer Pyle-like voice, and he had someone playing kazoo in the background who played a little ditty after every "Begin again". On the last verse (I think out of 3 or 4) the kazoo guy kept going and he say "Well...no, no, that's the end", "No, that's it.", "Oh, dog-gone **mumble** **mumble**", and as the song faded out "Well why don't he quit?" but the kazoo guy kept going the whole time. My sister and I thought it was hilarious. Somewhere in the song he even said the kazoo guy's name, can't remember what it was though...something childish like Wilber, or Ducky. I'd hoped to find it on YouTube to play for my kids, or that one of these blogs might tell me who the singer was...alas.
The lyrics I remember went:

There was an old man named Michael Finnegan
He grew wiskers high on his chin'egan
He shaved them off, but they grew in'egan
Poor ol' Michael Finnegan
(half-note pause)
Begin again

(Kazoo played for a frame: k'wiki-wiki-wew-wew, k'wiki-wiki-wew, k'wiki-wiki-wew-wew, k'wiki-wiki-wew)

There was an old man named Michael Finnegan
He shaved wiskers off of his chin'egan
The wind come up and blow them in'egan
Poor ol' Michael Finnegan
(half-note pause)
Begin again

(Kazoo played for a frame: k'wiki-wiki-wew-wew, k'wiki-wiki-wew, k'wiki-wiki-wew-wew, k'wiki-wiki-wew)

There was an old man named Michael Finnegan
(can't recall the lyrics here...
...but the end result is he dies)
Poor ol' Michael Finnegan
(half-note pause)
That's the end of'him

(Kazoo plays for a couple frames: k'wiki-wiki-wew-wew, k'wiki-wiki-wew, k'wiki-wiki-wew-wew, k'wiki-wiki-wew (repeat)

While the kazoo keeps playing, the singer says each of these with some pauses between each:
"Well...no, no, that's the end"
"No, that's it."
"Oh, dog-gone **mumble** **mumble**"
And as the song fades out "Well why don't he quit?"