I have some experience of Singapore, going there regularly.
The main issue with a short trip is the variable weather, which can reduce your birding time significantly. But usually, the storms are quite short.
All places are relatively easy to reach by MRT and/or bus (for Sungei Buloh and Bukit Timah), but for convenience, taxi does help, as it's quite hot and you will probably want to minimise the time you walk without birding.
Pulau Ubin needs a day as you need a ferry and taxi, but still, I recommend that place as the "easiest" to get the mangrove pitta and other relatively rare species in Singapore (Shama, Hornbill, gulls and other sea birds, in particular).
Sungei Buloh and surroundings needs probably a day.
Butik Batok and Bukit Timah can be done in a day. All other places can be done in half a day.
I would suggest to combine Pasir Ris with Tampines Park.
Let me give you another suggestions: Central Catchment area (for forest birds) for 1/2 a day, that you can combine with the Botanical Gardens in the afternoon.
I would only consider the other propositions (Japanese/Chinese Gardens and Mandai Orchid Garden) if there are good bird news.
Finally, in terms of safety, all the people will tell you that Singapore is SAFE la! Nothing to fear
