I think I would find a frame at the Dollar store that would fit my block with a mat. I would cut the mat in a non colour like white or black and put it over the blocks edge and frame. You can find some nice mat material in the scrap booking supplies at Walmart? A shadow box frame might be another option. I love shadow box frames because they enough room that you can add buttons or bling. you could also use your original idea and put your block into an wooden embroidery hoop for hanging?