Thanks for the replies to date: To clarify, I'm flying to Haikou, Hainan. I'll be flying nonstop from the U.S. to either Beijing or Shanghai, going through Immigration & Customs there, then connect to domestic flight to Haikou.
BTW TSA locks are combination, set by the user. There's a keyhole-like slot on the bottom which is where the security people are supposed to use their special key to open the lock if they want to see the contents.