Totally right to use those jinetes as mounted conquistadores: they used to be less noble men with at least some money enough to get to Americas, have a horse or two (not always best quality, just what available...) and some light-medium armour plus weapons.
However they were lethal against aztecs who fought on foot, were scared of those big and noisy beasts and died by hundered wearing fabric or nor armour when charged by just a little mounted men with steel and armour.
It was a not very heavy cavalry in the french gendarme type, but instead a very fast and maneouvrable one, very good for making several times charge-and retreat-tactics not getting titred.
I'm not certain about Malta, however, based on where it is situated I would expect that the most likely cavalry support would have come from Stradiot. These Greco-Albanian light horsemen were mercenaries adept at fighting the Turks, and were often hired by Italian and German princes and kings.