So, this is what I came up with. I traced each of the kids' handprints onto white paper. Then I cut them out. Using that as a pattern, I used my pinking shears to cut the fabric. Then I pinned the fabric to the shirt, and used my sewing machine (yes I actually have one and can manage to operate it enough to sew a line, albeit a crooked one), to sew around the outline of the handprint.
Then I got out my needle and thread (even more shocking, I know), and sewed on buttons for the eyes and little gobbler thingy. Last, I got some black puffy paint that I had left over from our pumpkin shirts, and drew on the feet. The pictures are below.