Having sat on an Ukulele, I decided the best way to avoid pesky repairwork would be to hang the instruments up where I can't crush them. This does the job.

I've included two versions of the object as STL. One has a thicker base in case your ukulele head ends up needing to go through a wall if you try to mount it on the thinner one. The thin version looks better, and for my instruments at least, I think would work even if I had mounted them on a wall instead of the top of a shelf as I did.

Included is also the Blender file for these, which should be better suited for editing than the STLs.

You will probably want to use a pretty high fill ratio to get the structural strength needed. Otherwise, it's pretty much slice and print.