Hardwood edging is a great way to cover up the edges of plywood. And extra-wide edging is the best way to ensure complete coverage. The challenge is removing the excess so it’s perfectly flush without damaging the veneer on the plywood. If I only have a couple shelves and the edging is fairly thin, I grab my block plane. For the best results, set the plane to take thin shavings and plane with the grain. This keeps any tearout to a minimum. As you work, rest the heel on the surface of the plywood. You’ll find it only takes a few strokes with the plane to bring the edging perfectly flush.
When I have a lot of edging to trim or if the edging is fairly thick, I turn to a flush-trim bit and a shop-made fence clamped to my router table. The tall fence is just a piece of ¾" plywood. The fence face is screwed to a plywood base. And triangular braces screwed to the face and base help keep it 90° to the router table. Openings in both the face and base provide clearance for the bit.
You can see the bottom edge of the fence is rabbeted. This allows you to hold the workpiece flat against the fence while providing clearance for the excess edging that stands proud. Setting up the fence is easy. Just use a straightedge to align the face of the fence with the bearing of the bit and then clamp the fence in place.