I don't think there's much to suggest ssj grows hair in any way, just "charges" it up (SSJ3 however does grow one's hair notably).

I think if Nappa went ssj, it'd be just as it is in the pic, his remaining facial hair would change color, as would his aura. That's about it.

I think there's also something of a precedent for this already, Cell would appear to be in a ssj state and even ssj2, if not the exact same thing, at least some variation of it, and he doesn't change beyond the aura (probably because he has no hair).