Power Supply Regulation
You are testing a 'bunch' of LEDs, so what are you testing:


Go-NoGo
LED voltage at a constant current
LED current at a constant voltage
Optical output at 2,3 above


As Marcus pointed out you can regulate (make constant) either Voltage or Current but not both. 

I'd suggest you pick the parameters you want, and build either a well regulated voltage source or a well regulated current source. 

Since you have a reasonably well regulated power supply (one assumes it's a lab supply, you could simply create a small fixture and use an external INA226 board to capture the LED current and voltage, that would probably be accurate enough for rough batching. Here you would alter the voltage to achieve whatever current level you require and calculate the LED Vf