For singapore style laksa, you can try 328 Katong Laksa (postal code: 428770). The noodle served is cut into small piece. So you will use spoon to eat it.
Guess you may want to try Prawn noodle , you can try Beach Road Prawn Mee Eating House (which is on E Coast road but not beach road), Postal code: 428981. Be reminded to check if it is open before you go. They only open in the afternoon and do not open every day.