Can we travel on 144 hour Visa free entry.

We arrive from England, stop over for 2 hours to change plane in Hong Kong then arrive at PuDong airport 12.00 on 27 March. Stay for 2 nights in a Shanghai hotel then join cruise ship which leaves Shanghai port evening 29March. Our next port of call is Hong Kong, then Bankock then we finish and fly home from Singapore. We have British Passports and onward departure cruise tickets.
Can we apply for 144 or 72 hour free stay. If so which one please. Any other advice would be fantastic