No, there is no voluntary refund of partially flown tickets allowed.
T&C Section I point 13- KrisFlyer miles of completely unused award tickets may be redeposited for a fee provided the KrisFlyer miles and the ticket are valid at the time of redepositing. Any taxes will be refunded. KrisFlyer miles cannot be refunded for partially used award tickets and upgrades.
Ask the agent if they can split the PNR into two separate one-way bookings, since the cost is the same (i am not sure if it can be done though; i only know they can split pax from the booking, but not about splitting segments). Suspect they will tell you to cancel and rebook. Actually if the Advantage award for SIN-PER is still available, the best bet is for you to cancel and rebook - you only pay the USD 50 redeposit fee and you can get back your PER-SIN miles, presuming that no miles have expired. All this can be self-service done online yourself without needing to talk to an agent.