you could do raw-edge applique with paper backed fusable- you draw your peices on the paper- press to the wrong side of the fabrics- cut out- fuse onto the blocks then stitch around the edges.
you do need to cut your blocks (for the appliques) a little larger than they are called for- the trim them to size after the applique is stitched down- regardless of technique you choose- applique- just like embroidery draws up your fabric a little bit- if your blocks are to be 6 1/2" cut them 7 1/2" then after appliques are sewn down trim the blocks to the 6 1/2" size you need (or what ever size they should be)