It’d be all through intake, not exhaust. That’s where you get all the sucky whoosh noises sound from. Anything from the exhaust will be too explosive. Effectively, harnessing the sound of air being dragged into the engine for combustion, not being banged out.
The original sound was inspired by the sirens attached to Stukas in WW2, the siren wailing as the plane dove and air rushed through. These were added simply to terrify people.
However, there is rotaries. Adding rotary blocks to a rotary engine will make a much smoother scream sound, like the V10s and V12s of earlier Formula 1 cars. Though, it will be lacking that open air sound. Maybe with the right exhaust and intake, a tone could be achieved.
If you went EV, electric motors are high-pitched unless very large. You could combine this sound with air vents—catching air like the Stukas’ dive bomb air sirens—to get something similar, however, the air vents will be dependent on making noise with constant speed, disassociated with the engine. The TIE fighter also has no electric noise, it’s all terrifying roar…well, whatever the inhaling version of a roar is.