feedback ammeter vs current probe?
I assume the load takes large current pulses but with a low average current.

If you just need the average current you can use a normal ammeter (i.e. measure a voltage across a shunt) but add a large capacitor across the shunt (or across the load).

The capacitor will supply the current during the pulses and will let you use a shunt appropriate for the average current, not the peak.  The capacitor may need to be many hundreds or thousands of microfarads depending upon the particular scenario.