Okay, but the realities are:
That's why it's a challenge and not a what if. I didn't think it was likely.
Okay, but the realities are:
1) The US, UK, and France all had far greater economic ties with Latin America and vice-versa in the 1930s than Germany or Italy did with the Latin American republics;
2) The US and UK all had far greater abilities to project power (military, economic, diplomatic, and political) into Latin America than the Axis powers did;
3) The US and UK in fact, did project power (military, economic, diplomatic, and political) into Latin America during the 1930s and 1940s; the Axis did not because they could not;
4) The Latin American republics all gain from an alliance with the US and UK; they do nothing but expose themselves to heavy loss if they ally with the Axis powers.
IF the world is anywhere close to history as in terms of a world war in the 1940s with the US and UK as allies or friendly neutrals in response to anything resembling an Italo-German alliance, there's no way it makes any sort of sense - strategic, economic, diplomatic, political, or military - for any of the Latin American republics to actively allign with the Axis.
It's more than unlikely; it's essentially suicidal.
Best,