Your wire idea may work ok. Does this need to be around one of the AC wires (ie just the Active line)or will it work ok wrapped around the entire cable, which in my case will be earth, neutral and active?
All that's needed is that there is some capacitance between the live (active) wire and the pickup wire, so either should work.
I remember making a device that used this technique around 40 years ago. One application was to find out which lamp in a string of series-connected Christmas tree lights had failed, without having to take all the lamps out.