First you would need to measure the DC voltage across capacitor C11(markings 470,10V,VT) near resistor R4, with mains supply ON(so be careful !!!). The whole circuit board might be HOT(Live).
I would guess it would be either around 3.3V or 5V. You can then removes the board from mains connection and connect the external dc supply with approximate same voltage across this capacitor to power up the rest of the circuit. Measure the idle current, and you may need to cut off some circuit tracks if the idle current is too high. Let's do it a step at a time.