I'm not Singaporean, but I've lived here for 3 years...I hope I'm not disqualified from answering.
back when i didn't know anyone in singapore, one of the first people I met was a traditional artist who carried his easel and giant leather folio around with him everywhere. so i never picked up on the attitude that singaporeans were uptight about people sketching in public...me and this guy have sketched at mcdonald's, by esplanade, walking down orchard road stopping every few meters or so, on the train...I was probably introduced to singapore culture the wrong way by this guy, so it never really bothered me to sketch by myself in a public place. i even get occassional nice folks at coffee shops who'll start a little conversation because they're curious about what you're doing. there's going to be some people who find it strange, but for the most part, it's fine not to care about what random people in public think. it isn't strange at all man, it's only drawing.