A current transformer works very well with AC like that.
The thing to remember is that it is a CURRENT transformer not a voltage transformer, so you must not leave it open circuit. The output current is set by the input current and the turns ratio. There is a maximum output voltage that you can take. The transformer specification should say that.
It is quite easy to wire the output to a bridge rectifier, then a capacitor and a resistor.
You get much less power in the resistor for the same voltage drop, and it is much safer.