Most SMPSes have a current sensing resistor at the emitter or source of the main output device. Just scope across that.
If it doesn't have one, Charles is right, you can add one. You must however think about two things, one is that it must be a small resistance, and two if the chopper is bipolar, you need to make sure that degeneration of the drive current does not occur. What's more if the chopper is bipolar, you need to figure that some of what you're seeing is base current. It is not advisable to do this at the collector or drain, it's a shock hazard and radiates too much. You can't go to the AC rectifiers because of the nature of the signal you need.
I cannot completely agree that the current waveform of the chopper being parabolic indicates transformer satuation in every case. Certain time constants, snubber schemes and other things chosen by the designer could cause an innacurate conclusion on your part. I think you can get really meaningful data just from the efficiency. But then you might have your own reasons for wanting what you want.
I'd be interested in the application, or at least the capacity of this PS, is it like huge or something or are you trying to miniturize ? Just curious.