Don't you just hate the CLK and CKS designators.
Of course, I meant TPE Chiang Kei Sek airport... CKS...
No problem with interlining... just make sure that the UA agent tags your bag to HK all the way, and the CX agent at TPE will trace your bag and place it on the correct flight. Sometimes, you even remember to put the CX priority tag on as well.
Carfield