Well, if you are not sizing in between removal of old and insertion of new, you will likely run into the problem of the case neck being crimped into the old bullet and needing straightening out. It will still mostly be in the crimp position after pulling the bullet. Otherwise you may be shaving jacket material off the new bullet, seating it crooked, and compromising accuracy as a result. Whenever I pull bullets with the intention to reload I neck size before anything else.
Bruce has the right idea in his post above, that is : Is your powder charge safe with the intended bullet? If the bullet will do the job required why pull it in the first place?
I assume that, like me, you have some ammo that does not meet requirements and you are attempting a salvage job. Just be careful and watch for pressure signs when you fire the first round of reloaded stuff. After the first found goes downrange this is a time for calm quiet reflection while you examine the case. Shoot no more until you have done this. Be safe.