Potential problem with hemming is keeping the wool outer layer longer than the silk lining, preferably without RE-hemming the silk. But I don't know know how much of a problem that is (cloak is at home, I'm not).

If I try for a non-hem solution, there's GOT to be a more elegant way than fraycheck or glue. Trying to full/felt the edge comes to mind, but that might be way more complicated than my first guess makes it out to be.