Oh, the nostalgia!! This was one of my favorite books as a kid, and I just recently bought another copy to re-read.
Instead of a stencil, you might want to try carving it as a rubber stamp (I might have to try it myself!). If you make a photocopy of the image and iron it onto a carving block (like Staedtler Master Carve), you'll have an excellent image to start with.
Then, using an exacto knife, CAREFULLY pre-cut around the lines (this makes it much simpler to carve out the pieces later). Then, using a set of Speedball carving tools (they come in a pretty inexpensive set- 1 handle, with interchangable tips), carefully carve out the rubber that isn't printed on.
It might take a bit of time and patience, but then you could stamp it on a whole bunch of things (some stampers say, "If it doesn't move, stamp it!"), especially since there are so many inks available (even fabric inks).
I think I might have to bookmark this so I can "borrow" the image!