To answer your specific question, no, I would never use an axle shaft to drive a bearing on or off. Hardest thing I normally use, is plain cold rolled steel. Even then, it is important to properly grind and maintain the mushroomed ends, if you don't, pieces could fly off and hit you in the face (can and do). Why would anybody use something even close to the hardness of a bearing, to drive it on or off????
*** Disclaimer ***
As I have no wish to toy with anybody's life, I suggest you take this and all other posts with a certain amount of skepticism. Carefully evaluate, and if necessary, research on your own any suggestions or advice you might pick up here, especially those from my posts, as I obviously haven't the skill and experience exhibited by some of the more illustrious and more successful members of this forum. I'm not responsible for anything I say, as I drank toxic water when young.