Whatever you use must be "Class 2". That means there is not enough power available on the secondary to cause a fire. Using a class 2 transformer allows using light weight thermostat wire instead of power wiring.
Class 2 heating system transformers can be easily installed to be safe, with primary wiring not exposed - may or may not be true of the transformers above.
Modifying a class 2 transformer by replacing internal fuses with external fuses makes the source not class 2. If you knew what you were doing you could probably protect the secondary with a fuse. I wouldn't.
I agree with looking at the secondary current.