Step 2: Brace yourself
Let's build a Y-shaped rod that is divine.
From the wood scrap pile, grab pieces that are long and narrow.
We need to build the internal frame structure. It needs to be able to resist the pull of the launching band.
Cut up and mock up your pieces into the desired shape.
Try to overlap the pieces at the Y intersection.
Glue and fasten with fasterners if you can. I predrilled so as not to split the pieces when the screw is driven in.
Reinforce the pieces with more wood strips glued on.
Start wrapping and gluing strips of corrugated cardboard. You can slightly angle the wrap and squeeze down to compact the papier mache. This all adds to the character of the "wood branch" when the glue dries.
Staple one end to fix the end of a strip of cardboard. Wrap around tightly.
The strips will randomly give variations in branch thickness adding to the realism of the final product.
When you get the desired thickness, bridge the major gaps in the cardboard strips with another layer of cardboard to smooth out.
Since I was not going to paint this when finished, I used a mix of gray wrapping paper and brown paper from a paper bag to form the final layer. Tear in random pieces and papier mache. This would give a mottled sycamore type bark effect. Feel free to simulate the local native species of wood.
When completely dried, it should be a fine looking scion, with the nut that fell from the tree standing next to it.