Beginner Q: Measuring current via USB charging cable
One way or another, you'll have to break into your cable.

USB cables are cheap.  Get a short one just for this purpose, especially if you want to do this more than once.  The best would be one of those USB "extension" cables with a type A plug on one end and a socket on the other.  These things are not good for the USB signal, so get the shortest one you can find.

Very carefully cut open the outer jacket of the cable.  That should expose four separate wires.  Finding which is which might be tricky.  Worst case, expose a little bit of the bare wire of each, then use a ohmmeter or continuity tester to see which is connected to which pins of the plug.  You can look up which plug pin is which conductor.

Cut the power wire and solder about 100 m&Omega; in line with it.  Bring out connections to both ends of the resistor.  Now fix the cable by using electrical tape or hot glue.

At this point, you have a regular USB extension cable with two wires coming out of it from the middle somewhere.  Insert the cable in-line with the device you want to test.  Connect a voltmeter to the two leads coming out of the test cable.  The voltage will be the power current times the resistance you added to the cable.  For example, if you added a 100 m&Omega; resistor, then the voltmeter will show 100 mV for every 1 A of current.