I’m in the process of designing a CNC/Lasercutter case for my Beepy Here, only the part above the PCB is wooden. I cut it with a Glowforge laser cutter using medium draftboard (about 4mm) and walnut veneer. The back is a 3D print of the bottom half of the Beepy slim case.

The SQFMI folks make Step 3D models available. I used it to create the the plate that sits on top of the PCB. I created a 2D projection of the top of the slim case to create the cutting file for the veneer. If you have a laser cutter like a Glowforge, these SVG files might be useful to you (you’ll probably need to “Save Link” from your browser since these will likely render):

This is very much progress – ultimately I’d like a wooden back as well – though it’s actually fairly nice as is, so I’m posting it here. Of course, your mileage may vary.