Here's a simple 10mA current source you can use to measure the forward voltage of your batch of LEDs:
View attachment 141732
Current is set by R2. I assumed a forward voltage for LED1 of about 2.5V so 180 ohms will give about 10mA.

You can use some sort of socket to insert the LED being tested between the collector and ground. You can place your DVM between those same points so you just need to keep swapping LEDs and binning them by forward voltage.

Vf does change with forward current and your circuit will do a precise job of measuring the Vf with a constant current. Though, if you keep the current in a range, say 9-15 mA, then the Vf measured will be reasonable and can be used for specing out the resistor for the strings. That's what the circuit I posted does and uses common resistor values, depending on voltage source. LEDs are pretty resilient if you keep well away from abs-max values. I'd bet anything under 20 mA would be ok for no-name LEDs, presuming a Vmax of 50 mA or higher.

I would recommend measuring the current of the LEDs in each of the strings just to make sure.

 

I'd bet anything under 20 mA would be ok for no-name LEDs, presuming a Vmax of 50 mA or higher.

Absolute maximum forward current for the white LED I cited above is 20mA; forward voltage is characterized at 10mA.

 

A quick jig - tape 2 paper clips to edge of bench in the shape of a shallow V bridged by 2 red LEDs in series then connected as DUT ( device under test ) in d1324 CC ckt. post # 20. If test LED is reversed in testing, the 2 RED LEDs limit the reverse V to 4 V, if correct
polarity, Red's are off.
In checking some, found several 5mm with rev. polarity- anode short lead, 1.8 V,
Tex. Inst. TIL 209 red 3 mm = 1.7V @ 10 mA from 1970s. , square green 2.03V .
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