A shunt will be your best option for light AC loads for up to 200mA, applications using a CT is used for anything AC above 1A and more (generally).. Also the CT noise floor and gain used to sample currents as low 50mA AC with say a 10mA resolution seems unavailable.
That isn't even in the ballpark of what you can do with inexpensive CTs these days. As I said before, a cheap modern CT can measure 10mA to 100A with an accuracy of 0.1% of reading across the entire range.
10mA to 100A...inexpensive CTs?, I cannot seem to find them on the net.. care to share an example of one?
Try looking for CTs made for the utility meter market, from companies like ShengKe. Less than 50 cents in quantity, DC tolerant, and measuring up to 60, 80, or 100A, depending on the model. There are also CTs made for operation up to 6A, for use with a multiplier CT outside the utility meter. These are very standard parts in the utility meter market.
If you want to see the kind of results you can get with those CTs in a meter design, try looking at app notes for utility meter devices, like
http://www.ti.com/lit/ug/tidu291/tidu201.pdf . The tests there only go down to 50mA, but the accuracy doesn't degrade much down to 10mA. That is 10mA to 100A measuring active power to an accuracy of about 0.1% of reading. If you want to measure RMS current, the noise in your analogue front end can spoil things a little. However, if you properly subtract room temperature AWGN during the measurement process you can measure RMS current down to 10mA with not much worse than 0.1% accuracy. If you measure RMS current in a more bull at the gate manner you may be down to a few percent accuracy at 10mA.