You'd best be using an op-amp with some kind of transistor most likely. And a precision voltage reference and a few precision resistors. You will only need a few volts of compliance since the Si diode won't drop more than that, and the drop across the high-resistance cryostat wiring should be negligible at 10uA. 

Plus another op-amp or two to buffer and amplify the voltage to your ADC, in this case an instrumentation amplifier with +/- supplies would be a good idea to return the signal to ground reference and amplify/buffer/signal condition. And some more precision resistors. 

And likely some circuitry to make sure the amplifier output does not exceed the input bounds of your ADC and protect it from damage. 

Or just buy an instrument designed for the task from Lakeshore or whoever.