I don't think it is worth measuring the diodes unless you are going to use them for a very specific purpose. But in that case, you really do need to know max current they support, and what current you need to get the light intensity you want.

If the above don't matter, all you can do is guess. You may guess that they support 5mA current. You may guess that they have 2V voltage drop. You may take 12V and compute a resistor for this condition. measure the actualy voltage drop over the LED. Then decide what current you really want to send through the LED. Now, if the LED does not support 5mA, then the above test may kill it. You could do the same thing with 1mA instead. It will give similar results since the voltage doesn't vary much with the current.

But knowing the exact voltage is only important if your supply voltage is very near the LED voltage so there will be a very little voltage drop over the resistor. Then a small calculation error for the resistor will result in a large difference in current through the LED.

In the end, the resistor is important since it not only limits the current through the LED but makes sure that the current through the LED will be almost constant even if there is a bit of variances between indiviual LEDs or in the same LED depending on temperature, age, ...

Obviously it will matter a lot if you try to drive two LED in parallel - but that isn't something you should do anyway even if you have hand-screened the diodes and selected two with the same Vf. They can still diverge at a different current or at a different temperature, in which case one LED will get way more current than the other...