I doubt you'll have any problem carrying a Swiss army knife or leatherman type tool, they sell cheap replica knives like that all over the place, so it's a pretty common sight. I've also carried a sword around the streets of hong kong, nobody gives it a second look.

I would definitely recommend a small button compass or something similar, just because it is really confusing in the city when you get off a subway. I would skip the water purifier, it's probably not necessary unless you plan on going camping, you'll find bottled water all over the place. Both cities are very modernized, so the stuff you carry should probably be more focused for an urban environment, you probably won't need the wilderness survival gear while you're there.