From Hangzhou to Shanghai, because you would like to arrive early, it is suggested that you take the train K135/K138 (07:07~08:45, 22RMB) or D5654 (07:40~09:08 53RMB).
From Shanghai to Hangzhou, you could take the train back too, there are several trains for your choice around 12:00. Please search the time table at https://www.travelchinaguide.com/china-trains/

There are also frequent buses between them, but the bus fare is CNY68 per person and take 2 hours on the way.