Remember that spectrum analyser can work without cable, just with antenna ?
You can make an air core ("plastic"styrofoam core") transformer: draw a 10-15 turns spiral on a board and terminate it with high-Z load. Glue an insulating pad on top of it and slap a 3-5 turns of insulated solid wire soldered to BNC connector. Cover everything with pile of glue.
Connect spectrum analyser to this pickup coil and you are done with impedance/overload/grounding problems.