Primitive Gatherings uses only wool; and I am currently working on one of their block of the month. I am using Fray Check and it is doing the job for me; but I try to put very little. Just run the tip of the bottle lightly around the edge of the piece. My friend is using the Steam A Seam 2 and is very happy with her results also. You can tell which pieces of wool may fray because the fibers aren't as tightly woven.
Good luck with your kit...that is a lovely gift from a thoughtful son.
Lucky You!!