powerwashing will definitely work, no doubt there. If it were me, I'd go rent a strong (3500 psi) power washer and do it from a distance (couple feet maybe, if you put it right up to the stucco you'll def crack/chip it). A hot water pressure washer would work better, but they don't have those where I rent stuff.
I'm sure that there's a bunch of chemical approaches that woudl be applicable too, but I'm ignorant of them so I can't tell you much about them. I'd just go rent the pressure washer if it were my house.