We've just moved to Singapore with our 7 month old baby. We have a car seat but it is totally impractical to take it around everywhere. What works for us is that I stap him to me in the Baby Bjorn, facing towards me. I then starp in ensuring the strap does not go over our baby i.e. wait belt under his legs and cross strap under the strap that holds him in on top.
Our thoughts our that in a crash his head would be supported by the carrier, there is enough give to cushion the impact and he is securly strapped to us and not loose in the cab (that thought terrifies me!).
If taking our stroller, we simply pop it in the boot.
As we are new to Singapore too with a baby of similar age, maybe you would like to meet up?