Measuring change in magnitude of electric current due to change in conducting material characteristics
All Voltage sources have an effective series impedance which causes drop in voltage with a rise in current. This is a step load regulation error spec.  The load regulation error with a transient, step load or DC load may be different if the rise time and inductance is significant Vdrop=LdI/dt but I doubt this will affect you. 

So you could define your worst case load ratio to total loop resistance  incl this path to estimate the load voltage regulation error. Identify all series R values in a current loop to estimate this result.

The load is TBD and so is your conductor, so a sensitivity to tolerance variations depends on the initial contribution to this step load error and each individual path.

Once min,max current is defined with tolerances to voltage error, you can define an acceptance criteria for tolerances.

Keithley might be your best source for pA magnitude measurements. Unless you can manage to raise Voltage enough to measure with a current source or high series R  gigaohms.