Replacing Radiator, should I replace it THEN do an engine radiator flush

I'm not a fan of any chemical flushes. My dad always used a heaping cup of cascade powder. Drain coolant. Cup of cascade. Fill with water. Idle until thermostat opens with heater on. Drain and refill with water. Repeat idle until thermostat opens. Drain, replace radiator, New thermostat, coolant fill.
Dad's take was cascade would clean and rinse out easily.