Well, in the absence of the "original," I must admit my first thought (as a not-so-closet incurable parodist) was that "Roll, Alabama, Roll" might make a good version. Someone sang the "proper" version at Towersey so it is fresh in my memory--along, perhaps, the following lines:

These new deodorants kill B.O.
Roll, deodorant, roll.
They come as Ball or Aero-sole.
Roll on, deodorant, roll.

A smelly armpit is a dreadful thing.
Roll, deodorant, roll.
And how that perfumed stuff does sting.
Roll on, deodorant, roll.