Measuring 100uA should be easy, when I read the title, I though you might be thinking in terms of single digit nA or pA!
You don't mention what kind of dynamic range this is for, what accuracy, what resolution, or what sampling rate.
Is it to measure a low voltage power supply? If so, one solution is to place the shunt before a low Iq regulator: there are a number of LDOs that offer Iq in the order of tens of nA, so you can measure the voltage drop across a shunt in front of the regulator for the current range you mention. If you want to measure higher dynamic range, you can use two shunts in series, the sensitive one with a low leakage diode (or transistor as a diode with base & collector connected) across it, and take two measurements.
There are plenty of INA current sense devices, you need to figure out things like what offset is acceptable, what gain, accuracy, drift, directionality, high- or low-side, and how it's presented, eg as a voltage or as a digital interface like SPI or I2C.
I'm curious, you say it's a "fast test" and "not a project", what is wrong with a multimeter, or is this for your own academic purposes?