Honestly, I think it's very hard to do. Would seem simple on paper, but in reality, with such fast edges and currents as low as 1uA, any parasitic capacitances (causing unwanted coupling, charge injection) will mess up the shape of pulse. Of course, that's subjective, depends on how accurate you want it to be.
But that's just one part of story. What will be your load (current sink)? If the load is a low parasitic capacitance resistor connected with very short trace, then it's ok. But most likely you use it for something else. So if PCB trace is a bit longer and the load has some capacitance, then you current pulse will just integrate and not be a pulse you want. 5pF capacitance will charge or discharge only 20mV during 100ns at 1uA!
Maybe it could be done with a laser or LED coupled to a fast photodiode or something.