The Zambesi was described as follows in the 1961 Hohner London catalog:
How it got the name Zambesi is not clear. You might assume after the river; it was, after all, launched alongside the Hohner Amazon. However it was also launched alongside the Hohner Apache... which is not a river. But the popularity of the 1953 film Stand at Apache River may have inadvertently given the impression it was?
But the instrumental track Apache was an absolutely massive hit for the Shadows in 1960, and Zambezi (note different spelling) was an equally massive song of the time - written by Nico Carstens but widely covered, including by the Shadows (though they did not record it until 1964). But, there doesn't seem to be a record of the period to suggest the name Amazon (do you know otherwise?).
But Zambesi and Amazon were also names of British naval vessels of World War 2, and the USS Apache an American - could there have been a connection there? (HMS Amazon, HMS Zambezi, USS Apache). World War II was certainly high in the consciousness of all of Europe just 15 years after it all ended. In any case, to the British public of 1961, Apache, Amazon and Zambesi were all pretty exotic names!
If you know any better, or have your own theory, please comment