I feel 100% certain that the double sided tape wouldn't work.
What if you took a couple of pieces of wood and notch them out and glue them to the bottom of the CP with an adhesive that will bond wood & metal. Then you can slip the spinner in from the side, and use set screws from below to push the spinner up tight against the CP bottom?
Be sure the shaft will come out or slip all the way down before gluing the wood to the CP, otherwise the spinner wouldn't slide in with the shaft sticking up.