I have an idea, that, while not sturdy, will work fine, very cheap, and the only tool required would be scissors.
What you'd need is a broad strip of PET plastic (the type used in plastic bottles, or transparent packaging - "windows" on toy boxes to see the toy inside, slightly sturdier document sleeves, laminated paper documents etc. It has just enough flex it can be folded as you like, and is thin enough to be cut with scissor.
Make an inverse U shaped "bridge" between the two vertical supports of the wheel; two parallel length-wise cuts near the middle will provide a holder to hold the Pi case in place, and pairs of cuts near the ends will latch onto the wheel to prevent it from tilting.