You never really answered the questions about bandwidth, static or dynamic measurement etc. It's very tough designing at this level. If I understand it correctly, the 100K resistor will dominate. So, it almost looks like a voltage divider. As resistors get bigger, the noise voltage also gets bigger.
Another way of measuring very small currents is to measure charge, I did that too, but you have to select the mode, wait for things to settle ansd then zero and then count coulombs for say 30 sec or 1 minute and divide by the time.
You have to null. Read this: **broken link removed**
Look very closely at figure 1-26. Note the zero check function. Which basically shorts out the feedback resistor.When you do that, you basically get a voltage follower. If you short the input, you either get a "mess" or if done properly a way to measure Vos. Without some sort of series resistor in the inverting and non-inverting inputs, the output will try to saturate. a few mV across nearly zero ohms is a BIG number. The series resistor protects the OP amp.
With a little more work, you can add gain.
Of, course an automatic zeroing function would be better,
If this is part of say a QE system where your trying to measure the spectral response of the diode, a lock in and a monochometer would be the way to go. That's why I'm asking about particulars.