Here's what I've arrived at transposing Guest#'s first suggestion to C from Bb and making a few changes to suit the version I've heard.

Christopher Columbus - Chu Berry & Andy Razaf 1936

Intro |C / C7 / |F / Cdim / |C / Am7 / |Dm G7 C / |

[C]Mis[C7]ter [F]Christo[Cdim]pher Co[C]lumbus [Am] Dm] [G7]
[C]Sailed [C7]the [F]seas with[Fm]out a [C]compass [Am] [Dm] [G7]
[C]When [C7]his [F]men be[Cdim]gan a [C]rumpus,[Am] [Dm] [G7]
[C]Up [C7]spoke [F]Christo[Fm]pher Co[C]lumbus [Am] [Dm][G7]

[C]There's a land [F]some[G7]where
[C]Until we [Cdim]get [G7]there
[C]We will not [F]go [Cdim]wrong
[C]If we [A]sing, [G7]swing a [C]song
[C]Since the world [F] is [G7] round
[C]We'll be safe [Cdim]and [G7]sound
[C]Till our goal [F]is [Cdim]found
[C]We'll just [A] keep [G7] rhythm [C] bound

[E7]Soon his crew was makin' [A7]merry [D7]
Then came a yell, "Hey let's [G7]drink a toast to Isabelle
[C]This [C7]soon [F]ended [Cdim]all the [C]rumpus [Am] [Dm] [G7]
[C]Wise [C7]old [F]Christo[Fm]pher Co[C]lumbus [Am] [Dm][G7] [C]

[C]No [C7]more mu[F]ti[Cdim]ny.
[C]What a time [Am] [Dm]at [G7]sea.
[C]With [C7]di[F]ploma[Cdim]cy.
[C] Christo [Am]made [G7]histo[C]ry

[E7]Soon his crew was makin' [A7]merry [D7]
Then came a yell, "Hey let's [G7]drink a toast to Isabelle
[C]This [C7]soon [F]ended [Cdim]all the [C]rumpus [Am] [Dm] [G7]
[C]Wise [C7]old [F]Christo[Fm]pher Co[C]lumbus [F][G7] [C]