you could torch it off without issue.and, unless you're an idiot with the torch, you wont hurt anything beside the parts you're changing.
very little heat will transfer to the axle, and certainly not enough to damage it. it would have to be glowing orange to cause a problem.
Yes, as a former ASE Master Tech, and for the last nine years having contracted my services out to several professional racing teams, I am aware of what will and won't cause problems for the strength of steel when subjected to the high heat an oxy/acetylene torch can create.
Over the years, I've seen plenty of parts changers who were idiots. They had no concept of what damage their careless use of a torch can cause to the grain structure of metals, and their subsequent weakening, when subjected to too much heat.
Moderate heating and cooling of parts is very common to ease assembly/ dis-assembly.
It's virtually impossible to affect metal strength by cooling it with methods the average person has at their disposal. Supercooling metals using a process called Cryo-treating, is often used to increase the strength of metal parts used in critical applications.
Heating metal to the glowing orange state you mentioned to loosen or remove parts, is all to common when the lack of understanding of the potential damage being caused isn't present.
If they were to quench the metal with the appropriate method for the grade and type of metal in use, then the original strength could be maintained. Unfortunately, that almost never happens due to the lack of understanding, and the metal is just allowed to cool gradually, which results in softer/ weaker metal.