Just do exactly the same as you do now, carry some cash and use your card. Really, most of the world is pretty safe and easy so it's unlikely you'll run into too many problems, especially in Singas. Terrorism, banking system crash etc are unlikely but Orchid Towers will provide a safe space should you feel unsafe

Before i go anywhere i go get a few hundred exchanged (or ordered) at the local shops money exchange (the convience far outweighs a few $$ in fees or chasing a better exchange rate) and then just make sure your card works OS.
I've never seen a travellers cheque being used either so i'd avoid those.