Well it must have been a 2 seated plane because Polly perkins was in the back seat.It is after all a plane with grappling hooks that can go underwater.
Obviously, Sky Captain's plane is a P-40D, with the D standing for Dex, as Dex modified it from it's base model to include grappling hooks, a telegraph, magnetic explosive compartment, as well as wings that can sustain a much tighter turn radius than what would normally be possible without dropping flaps. And let's not forget the super engine that get's him up to flying speed without any evidence of torque. Seriously, if we get the plane from the movie, we might as well give the B-24s some jet engines and say "Nuts" to realism.