50Hz transformer being used on 60Hz power supply

I assume you meant reduce the fan blade angles a little? This is quite easy on most decent modern axial fans. My specialty is not transformers but since we are talking about 50 Hz transformers being used on 60 Hz power supplies - let's consider an example where we keep the VOLTAGE constant (We keep the Volts/Hz ratio constant. Say 400 V primary (secondary doesn't matter), with a volts per turn at 50 Hz) such that the core flux density is 1.5 Tesla. This will give certain core losses, of which a good portion is Hysteresis - plus copper losses of course.

We now use the same transformer at 400 V but at 60 Hz. The equation will show easily that the core flux density will drop to 50/60 x 1.5T = 1.25 T. The 20 % increase in Hysteresis losses will apply. But a quick look at losses in electrical steel will show that the core loss will now also drop due to the reduction in flux density. This will be quite substantial, and can be quantified by looking at transformer steel technical catalogues (that give core losses for various frequencies - against peak flux density).

Practically the result of this is that the transformer will run cooler on a 60 Hz system AT THE SAME VOLTAGE. Given the eddy-current and skin effects - even with these, it is highly unlikely that any 50 Hz transformer will not operate at rated load or higher on a 60 Hz power supply system at the same voltage levels.

Obviously the reverse does not apply because the 60 Hz (designed) transformer - assuming it has 1.5 T flux density for rated voltage - will end up at 60/50 x 1.8 T when connected to the same system voltage but at 50 Hz. This will cause many a modern (fully rated) 60 Hz transformer to overheat, due to the saturation of the core.