Hi,
Crest Factor = Peak Current / RMS Current. In a linear load, the Crest Factor is 1.414. However, in a general purpose SMPS, due to its non linear nature, this factor will be much higher - in the region of up to 4.
See if you can measure the current using a CRO/DSO by putting a small resistor but having higher wattage in line. Then measure voltage across it, adjust the scale of the CRO/DSO in such a way that V/R = I, you'll get the current in the CRO/DSO. Then get the peak value of it and knowing the rms, you can get the crest factor.
However, there are instruments which can measure CF.