Uni-T UT210D is a current clamp meter that can measure DC current with a 1mA resolution, but it is not very reliable in those low current range, both drift and the the earth magnetic field cause noticeable errors. For example rotating the meter 90 degrees throws off the least significant digits by a few counts. It's also mentioned in the manual, you have to zero the meter before each use, and make the measurement in the same orientation as when you zeroed it. Because of these issues, and because it can't see the difference between a normal disconnected load or a tripped fuse, it would be my last ditch option, because it "mostly works" without any physical connection to the system.
If your automatic fuse has something that moves on the outside, then interfacing with that may be a better option.