[Hand capacitance detuning receiver]
double-sided PCB with the two sides
not electrically connected?

My gut feeling is that hand capacitance (maybe tens of pF) is small
compared to the capacitance between the two layers of PCB (hundreds of
pF) and that the shielding effect would be negligible.

Now, "guard ring" style shielding (as used in high-impedance PCB
layout) might be worthwhile, but would be more difficult to implement.

Tim.