HK is the best bet for repairs for your situation. Seoul has some places which as a non-resident/non-Korean speaker will be too difficult to you find/explain the problem, and you won't save any money over HK, just faster service (whilst you wait).

None of the airports you ask about have repair shops, so you will need to do it in the city.

I had an out-of-warranty Canon camera repaired at the mobile phone/camera mall near Mong Kok KCR station (now called Mong Kok East MTR Station). Its just past McDonalds, walking away from the station towards Nathon Road.

They can have it done in about 2 days. Go to the repair shops on the 3rd or 4th floors rather than the sellers on the lower floors.

Sham Shui Po would be a bit cheaper, but which would be more difficult to find a respectable repairer for a non-resident/non-Cantonese speaker.

My camera had the same types of problems you are having and it cost 250HKD to fix at Mong Kok Centre.