By plate I mean the Aluminium plate on which the PCB traces for LEDs are glued. The metal Aluminium is isolated from the LEDs and from the rest of the circuitry. Whatever voltage is there it's capacitive coupling, and irrelevant for the LEDs.
PCB traces between LEDs are only on the LEDs side of the plate. The traces should be visible as soldermask bumps/reflections when you shine an external light under a proper angle. If not visible, test the connections between LEDs with a DMM on continuity.
Once you know how many series LEDs are there, you can disconnect the LEDs from the driver, then apply external DC from a lab power supply.
I would test each LED at half its nominal power or so, in order to find if there are any defective LEDs, because at very low current (when testing with the DMM), the light intensity might be misleading.
Unpower the lamp, and use a Li-Ion battery with a series resistor to test each LED, one by one. Use some sharp wires or probes, and attach them on isolated handles (if you touch only one end, the LED may light by capacitive coupling to Earth, which means hundreds of volts and can even damage the LEDs by reverse breakdown).
Typical voltage drop on a white LED is about 3-3.2V, while a charged Li-Ion cell is 4.2V. Read on the box the total power, then divide that to the number of LEDs to find LED power, so to find out max LED current, then to calculate the series resistor. Or you can just go with a safe bet of 50mA (20 ohms in series with a 4.2V Li-Ion battery). Power LEDs, they are very bright even at half power, so you may want to avoid looking directly to the tested LED, wear dark glasses or obdtruct the LED before testing.
Don't use a lab power supply on current limiting, use a battery. Most lab power supplies are not really floating (they would light or fry a LED only by touching a single wire (by capacitive coupling with the ground), plus that the lab supplies have output capacitors that can discharge very high currents through a LED even when a current limit is set (because in many supplies the output capacitor is placed after the current sensing). If you think your power supply has a true floating channel (most don't), then set it on 4.2V/50mA but also add the 20 ohms resistor in series with the lab supply, or else the output capacitor might damage the tested LED.