I love Singapore and have visited several times over the past few years, and never once have I had the slightest concern for my/our safety or had even the slightest feeling that we stood out, even when visiting the less visited parts; Singapore is just so culturally and racially diverse I think you'd have to really try to stand out!
I don't to what extent that is rooted in fact, and to what extent it's really about not having a scaremongering media constantly telling you you're about to get knifed, as we do back home.
Having said that, the very first time I went to Singapore was with work, and I literally knew nothing about the place, and yet instantly got a good vibe from the walking around it - I can't say that about many other major cities.
Thinking back, I wonder if the lack of graffiti, chewing gum all over the pavements and generally cleanliness that plague so many other cities has an impact on the way we perceive safety and risk (Singapore is without question the 'cleanest' city I've ever visited).