Is April a good time to visit Shanghai or is there a holiday at that time?

Yes, it is suitable for traveling, because the weather at the time is nice in Shanghai, not very cold and not very hot. Besides, there is Tomb-Sweeping Day and the Labor Day in April, on which people can have 3 days’ off. But the Labor Day (April 29, 30 and May 1) is very popular with Chinese people to travel and SH is one of the most popular and important travel destinations in CN, so it will be very crowded and you are suggested to avoid this fastigium.