You would be very surprised at how well a good summer suit can breathe. If you tell your tailor that you need a suit that you can wear outside in the summer, they absolutely will point in the right direction with regards to material and fit.
There is no type of suit that will breathe well in Singapore. You just have to suffer and hope you can quickly get to an sir conditioned building.
I wear shorts and a t-shirt about 360 days a year. Long sleeves and pants are reserved for weddings, funerals and avoiding poison ivy and insect bites.