If I may chime in. Anyone who has tried to straighten a bent steel rod back to perfectly straight knows it is no mean feat. You can get it close though. And that should be OK, IMO.
But, also in my opinion, it should be done properly. Trying to straighten out again up near the head by using an axle is less than ideal, I think. It would be best, and probably work best, if done in the jaws of a big bench vise, as someone stated earlier. Smooth jaws.
But just squeezing in a vise won't get it perfect.
If you had a small anvil and a light hammer, you could then gently tap it back to near straight.