Seoul to Beijing to HK, HK to Shanghai to Singapore

I'm a Canadian traveling around Asia and am planning to go from Seoul to Beijing on transit visa before going to HK for a day. That same day I'd like to travel to Shanghai from HK before going on to Singapore as there's a good flight cost, so can I leave Beijing to Hong Kong and then go Hong Kong to Shanghai in the same day? I know I will need to re-check on for a new flight in HK.