If you are willing to fly bkk-hkg-cnx you can fly CX. You can price it out on itamatrix.com and see if it works for you. Also, be aware that you may not earn any mileage credit on deep discount CX flights.
That's a bit of routing for an hour domestic flight. Unless you're set on using OW award ticket. If you're not, look at Thai or Air Asia (low cost but with add ons for everything). There's much more flexibility with times and pricing than CX/KA.
I had this same situation, and looked at the CX/KA option... But really for so few miles it's just not worth the trouble. The TG return flight in J is under $200.
ITA does return a HKG-CNX flight on CX (Dragonair) but those price ~$1,000 for RT. in any case I would just forget oneworld and buy a non-stop ticket on Thai or Bangkok airways for <$80 it's only an hour flight...
Programs: AA EXP, IC PLT RA, Hyatt Diamond, GE, NEXUS, SES
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You'd be a fool to fly BKK-HKG-CNX when you can get a flight on PG (Bangkok Airways) for practically nothing. PG is a great little airline and their flights are very reasonably priced. You would waste an entire day flying to HKG onto CNX when you can hop on a PG flight and be there in 45 minutes.