[whirnot]

There is a happy medium, if that's what you want. Not knowing if it is lacquer or not, I would err to the cautious and remove it. That doesn't mean you have to go to bare metal. There is also primer below it, and usually a fair amount of filler.
My preferred method is to sand off All paint, to the primer or filler, as long as the filler is sound, and necessary. You may or may not hit bare metal in spots in the process. I then prime with an epoxy primer sealer, fill anything necessary, prime with high build primer, block sand, repeat as necessary, then final sand and paint.
There is a ton of labor involved, and because Model A fenders are all compound curves, almost all the block sanding needs to be done by hand.
A reputable sand blaster can also blast with no issues, I see it all the time, just make sure they are experienced in doing car bodies. Then make sure you use an epoxy primer sealer first.