Would it be an historical mistake to picture the Spanish trading with ancient Mexicans to get the metals they wanted?
Depends. They need to adapt to the concept and art of metalworking first. Most likely is the same thing in the US/Canada occurs--the natives only request the finished goods, which are received, no doubt in exchange for gold. However, since the societies were far more complex in the Valley of Mexico than in the modern US/Canada, given a few decades and there'll be an indigenous metalworking industry (at least with the stronger states), assuming the metals are present and able to be obtained. The smaller/metal-poor states will probably still be dependent on importing finished goods.
I'm questioning Spanish strength in the Caribbean had they failed to conquer Mexico.
The native societies there were pretty rapidly dying due to both disease and probably the single worst case of widespread brutality Spain perpetuated. Since the time of
Columbus, the natives there were being butchered.
France and England would be a bit interesting, but I wonder about a filibuster by Dutch Calvinists technically subject to the Spanish crown, or the Knights of Saint John hearing about Cortez's failed conquest of wealthy pagans that sacrifice people and deciding to take a crack at them. Conquest by small fringe groups is possibly a lot of fun.
As for Spain: if you somehow butterfly them getting Mexico and Peru you're going to have a huge butterfly indeed. The economic shift alone would be staggering, as Caribbean cash crops require a bit of a different metropolitan relationship than massive gold deposits.
I don't know about the potential to conquer the region in one swoop like Cortes did, especially since disease is getting introduced one way or another, and I think the mortality rates (not the 95% historically but still huge amounts of death) combined with perhaps some European trade in weaponry will cause the Aztec Empire to shatter. It's in the interest of European merchants to have a divided Mexico. Certain states, like anything on the Caribbean coast, might get conquered in the long run.
But for Mexico's sake, a military conquest might be less desirable than trade in the long run, and we only have to look at the Dutch in Indonesia to see that wholescale conquest might be out of the picture and instead, grabbing some ports here and there plus protectorates and extensive trade a more logical operation. Mexico itself will probably go to hell for a few decades with repeated epidemics and extensive warfare amongst the states both already there and those emerging from the collapse of the Aztecs. Fertile ground for mercenaries and trade in weaponry and horses. Some mercenaries might be able to take over a state or two.
I picked Calvinists and hospitalers respectively because the Calvinists might translate the bible into the vernacular and the hospitalers were probably the best medical people available and would have tried to mitigate the epidemics. Interesting nock-on effects either way.
Nahuatl language fluorished in Spanish Mexico though, as did Quechua in South America. Spain actually helped spread Quechua, and I'm not sure about Nahuatl, but I wouldn't be surprised there either.