You really can do that on your machine but it sounds like you just might rather want to do it by hand. If you do decided to try it on the machine, I would practice first with a couple of different stitches, and stitch lengths - blanket and satin. You might find you like one better than the other. I know I did one applique recently with a tight satin stitch and now I really don't like it.
Good luck - take a picture of your work when it's done for us to see!