Measuring current with an osciliscope
You don’t need a specialist current probe for your osciliscope as you can simply measure the voltage across a current sense resistor. This is a typical test measurement method and can also be used to measure the current of very fast pulses.
A typical test for current is to use a 1k resistor and an oscilloscope across it, (with a capacitor added across it to dampen if needed). If your test can handle the 1k resistor then it’s nice because 1V measured = 1mA of current (I = V / R).
However there’s no need to use a 1k resistor, you can use any value, with a 1ohm resistor being a good choice when not wanting to add significant load. In this case, 1V measured = 1A of current, 1mV = 1mA (I = V / R).