My solution to this issue is to prevent the fraying even before I cut my cloth. To do this I mix a small amount of white glue into some water. It should be some what thin. I lay my cloth flat on a nonporous surface and draw my cutting lines on the cloth with a pen or chalk. I then take a paintbrush and paint the glue mixture over my cutting lines. I allow it to dry fully and then cut the fabric as normal. If you cut before you treat, the cloth edges will wumple up as it dries. Painting the lines on before cutting prevents that.
Note that I do NOT use fraycheck, or other types of liquid stitch products, as they can eat away at silk. Also, if you drip it onto the cloth, the cloth will forever have a spot on it, whereas you can use some water to further dilute the white glue and get it out of your fabric before it is damaged. Plain white (elmer's) glue also has no fumes.