If I were to undertake this project, here is how I would do it. Cut the wood into desired shape, then saw off both the top and the back. This will allow you to remove the interior in one piece, using either a band saw (entry cut covered by an end graft) or the hard way with a coping saw. The secret to a nearly invisible glue line is to not disturb the original saw lines when gluing the top and back on. As Chuck pointed out, the end grain portions will need to be left thick. Expanding on the concept, instead of gluing the top on, you could hinge it. Take the off cut from the center and make nesting ukuleles from one piece of wood.
Brad