Yes, I would cut the leaves that have the rot on them. Use a flame-sterilized & cooled cutting tool, cut into green healthy tissue between the plant and the rot. Leave it go for a day or two, dry, in the shade, so the cuts can heal. Resume careful watering (roots only) afterward, watch to be sure the rot does not return.
how far into the crown does the rot extend? I'd be inclined to slice it off as well.
You should then treat the plant, I personally use Potassium Phosphite as a rot preventative, if you can get yates products in Singapore look for Yates anti-rot.