At a recent chantey sing in NYC, I sang the Hagar Man because Ken Schatz was present. He lost it.
When someone retires, Jan and I generally do:
"When I retire in due time,
    Way down to Florida,
My Miami condo will be divine,
    And we'll roll the U-Haul down...."
We always throw a cheezy Yiddish accent and crack up the crowd.
On the other hand, using a melody instead of writing your own can be a sign of laziness. Gordon Bok and I went round and round about this for a while.
An example that I frequently cite is that Pete Seeger's "How do I know my youth is all spent..." is very similar to "Officer Krumpke" from West Side Story. When I asked Pete about this, his comment was they were probably both descended from "Fair Harvard." In other words, everyone does it, whether or not they are conscious of it.