I've always had hotels supply lots of free bottled water, which I drink, but I use tap for brushing teeth, etc. and do not obsess about the possibility of swallowing water in the shower the way I do in places where you should not drink the water. I'm not sure whether I would worry about ice cubes in Hong Kong; I can't recall ordering an iced beverage but I think hotel rooms have ice buckets which are filled at turndown.