You could do prepared applique with no fusible product whatsoever. It involves cutting your applique pieces to include a seam allowance (typically 1/4 or less) which you turn under and press in place (or you can glue them down using a washable glue, like elmer's school glue) then machine stitch the prepared applique to the background using a blind hem stitch.
Another option is to use a machine satin stitch to encase your raw edge. Cut your your applique pieces and apply them to your background piece using pins or drops of elmer's school glue or other washable glue. You will need to put a tear away stabilizer of some sort under the background piece, otherwise it will pucker from the satin stitch.
A final option is a raw edge applique that will fray, kind of like a rag quilt. Cut your your applique and top stitch to background fabric about a 1/4 to 1/8" in from the raw edge. The edges of the applique will fray with washing.