So... it seems that we're discussing a variable current source with a maximum compliance (ie, open-circuit optput voltage) of 1kv. I assume this would be to test the arc-clearing ability of the fuse under test. It's not clear though if this is AC or DC - clarifying this would help.
Surely the ideal solution would be to simply place the sense shunt (or add an additional shunt) on the low side of the supply, so the voltage you're measuring is relative to ground. If you add an additional shunt, then you can size it to give an appropriate voltage swing into your data logger. It might be prudent to include a large series resistor and a zener to clamp any transients that may get picked up, but no high voltage clamping should be needed. If your supply really has a compliance up to 1kv then the additional voltage drop across an additional shunt would be completely irrelevant.
If we're interested only in the maximum current passed during the test, you may also wish to include a peak-hold circuit; this would also make the system suitable for AC.
You could then use a comparator circuit to detect the rise in voltage across the freshly-blown fuse and trigger the data logger (this would require good input voltage clamping, but with a high-impedance input this would not be a big problem)