144 hour visa without entry when you have a valid visa?

I'm travelling to Shanghai from London, spending one night in Shanghai and then flying to Japan the next morning. I will spend a week in Japan, and then fly back from Japan to Shanghai, spend 6 days in Shanghai and then fly back to London. I have a Chinese visa with one entry left on it. Can I apply for a 144 hour entry without visa for one of my entries into China? If so, which one, the first one where I'm spending less than 24 hours in Shanghai, or the second entry when I'm spending 6 days there? Thanks!