I'm no expert, but what is the noise you see if you just short the scope probe's ground to itself? Using the ground clip, my scope in x10 mode is similarly noisy to your graph, while if I use the little mini spring ground instead of the big clip, the noise improves from ~16 mV peak-to-peak to ~8 mV (again, just shorted with no DUT).
Maybe this a case where your test setup could use extra EMF shielding? I'll have to track down a cookie tin to make a shield and try out for myself sometime.
I also wonder about using x1 vs x10 mode to improve noise -- although you'll have to consider if the reduced bandwidth of x1 mode is enough to characterize your DUT's current fluctuations. I'm not really sure, but maybe worth trying.
Edit: Come to think of it, the bandwidth of the uCurrent is probably way lower than any x1 mode limit, so nevermind that!