Unwanted capacitance in measurement setup - what to consider?
Use a star point for ground; with such small currents, the smallest impedance in the wire will distort your measurement.
Terminate your coax cables properly; your coax cables are highly frequency dependend when you don't. 
You might want to use a high impedance amplifier near the device under test (DUT), like an active probe, FET-probe or something similar to drive the cables.
When measuring such small signals, you might want to try to change the setup into a bridge https://en.wikipedia.org/wiki/Wheatstone_bridge