Since Jim's put up the sheet music version, here's the other version from Crosby/Valente, with the very slight differences in the Poirot version in parentheses.

Mick

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HINDUSTAN
(Oliver G. Wallace, Harold Weeks)

Verse:
Here's a song, a tantalizing, ditty.
The tune is catchy and the words are witty
Could be it's a country or a city.
  Is it Tokyo?
    No, you gotta work South a little
  Is it Cocomo
    It's East, babe, move East (No you gotta work East now boys)

Here's a clue, the setting's oriental.
Has a native beat that's fundamental.
That came way before the continental.
  Is is Mexico?
    Nunca, senorita (Nunca, nunca).
  Is it Borneo?
    You're getting warmer, cos it's:

Chorus:
Hindustan, where we stopped to rest our tired caravan,
Hindustan, where the painted peacock proudly spread his fan,
Hindustan, where the purple sunbird flashed across the sand,
Hindustan, where we met and the world began (Hindustan, where I met him and the world began)


Source: Bing Crosby and Caterina Valente (after Bing Crosby and Rosemary Clooney), youtube as above. Bracketed variations are from the Poirot episode. The Crosby/Clooney version seems to have the responses used by in the Poirot episode, except babe instead of boys in the East line.