Hanging unframed stained glass-type panels
The glass bits around the edge are not fully encapsulated without a frame. This is a risk -- damage and / or injury.  I would recommend taking them to a picture-framing business and seeing if you can't get a reasonably cheap metal frame cut to size.  Obviously you wouldn't need a matte :-), but you might want some extra pads/shims to keep the stained glass panels from rattling in the frame.