The Shaker boxes I’m familiar with are elliptical in plan view and made of thin pieces of solid wood with the ends being tapered to create a long scarf joint so maybe I’m not thinking of the same thing.What I think you are describing though can be shown in an exploded sort of view but you can only insinuate the joint in the assembled box by drawing edges. It won’t actually separate the ends like they would be in the real material.
Here’s what I get from your description. Does that show what you have in mind?
If that’s it, I used Offset to create a circle on the rim of the box 1.5mm in from the outside. That represents the face of the lap joint. The ends are made with the Line tool drawing from that offset edge to the inner and outer edges. I drew a vertical line down the box also to represent the end of the piece. Then I erased the unneeded part of the offset edge. Again, this won’t really divide the geometry.
FWIW, this is what I generally think of when I think of a Shaker box.