I don't have luck wire wheeling paint off, it kind of heats the paint up rather than removing it. I think with good paint on the rest of the car I would sand it all off, it's dusty but it won't damage the exterior paint in any way. DA most of it and hand sand where the DA won't go. Before doing anything though liberally wipe it down a couple of times with wax and grease remover, don't be frugal with it.
That's how I did this one. I had the car painted and then drove it 500 miles home, tore out the engine, rebuilt it and painted the engine compartment.

Sheldon