Basswood would be a good way to go with this. it is cheap and friendly to carve. Buy a couple pieces, butt-join them into a rough L-shape clamp it until the glue dries. Saw out the shape with a coping saw (cheap), work out the details with a combination of rasps. If you have access to gouges or a router, all the better. Sand it up to 220 grit. Predrill a hole and run a couple wood screws from the grip to the body to secure the joint. tack in a trigger and trigger guard with finishing nails. (too much trouble to carve it from a single piece) To get the bow, you would steam-bend a strip of wood and lock it into a bow-shaped jig for a couple weeks. fix any flaws either with Autobody filler putty (Bondo is the common brand name) or wood putty.
Seal the wood with sanding sealer, sand again, prime it, paint it matte black.
I'd leave the string off altogether for safety's sake.