I think you have your wardrobe about right. I’m a regular visitor to Singapore for work. As stated by others, Air Con works overtime and makes places feel like a walk in freezer. Keep a cardigan with you at all times.
Unless you intend to commit a crime, ”Conservative Singapore” is something of a myth outside of Little India and the Arab quarter and you can wear what you like in most places. The myth is further demonstrated by the number of openly lesbian couples you see around Clark Quay. There is also the largest female only club in Asia on the Outram Road.
Although Singapore is not cheap, there are some great clothes bargains to be had in China Town, especially the markets. so save some room in your bags for new things.
Finally, remember it is likely to rain for some of most days (often in the afternoon) as well, so you need to cater for wet weather, humid weather, hot weather and freezing AC.