These LEDs don't cost you too much do they? Get new ones with specifications. That's what I'll do.
If you trust the guy you bought them from, with the 0.5W rating, you could use some variable power supply, a few fixed resistors and a voltmeter to find out what what voltage current value the LED works at 0.5W. with a serial resistor, say 300ohm, increase the power supply voltage and measure voltage across the resistor until you get V_led*I_led~=0.5W and stop there. I made my students do this on regular diodes but they could use a function generator and a two-channel oscilloscope. I wouldn't waste that much time for cheap LEDs.