When my iPod had problems, I took it to the Apple repair place in Causeway Bay, but that was because it was still under warranty. If it's out of warranty there are probably other places that will do repairs for less. Try asking one of the Apple dealers and see what they say.
I am sure you can get a battery replacement in SSP, there are some Mac enthusiaist shops hidden in SSP. However it is located in shabby, old shopping malls. Not sure how much it costs though, as I am not a Steve Job's fan and don't own one. But I am sure it must be a lot cheaper than what Apple Service Center commands.