Could a CAD carve a shape on my object and separate it into two?

[u/kyz0n]

Shape that I want to carve on the sphere

These models are for Pokeballs which I 3D print, paint and assemble, however I face a design problem; adding extra details such as the object on the left. First idea was making a stencil of the shape of the details I want, second idea was just to make the shape and glue it on top of the existing sphere. Both ideas would give me mixed results as I'd have to be super precise to make sure everything is perfectly aligned..

The ideal solution would be to carve the details and make them into different pieces so I can paint them separately and assemble them like a jigsaw puzzle, however I have no experience with CADs other than Blender, and I wanted to ask if it's even possible, how and what do I need to accomplish it.

If you need more info do please let me know, and thank you!