Disneyland is in Lantau Island, as you said, you also want to go to Ocean Park, which is on Hong Kong Island, Chung King Mansion is at Tsim Sha Tsui, this place can reach both of your destinations easily, if you don't want to ocean Park, then forget it. About the safety of Chung King Mansion, it is unsafe outside the hotels, but there are safeguards when you enter the hotels, this place has the most affordable hotels in Hong Kong. As you asked.
Maybe you can stay in the Panda Hotel, it is located at Tswen Wan and it's easy to reach the MTR Station from the hotel. Traffic is also convenient.