Cut hardwood plywood panels to wrap around the unit. Make the top and bottom panels long enough to cover the side panels, and cut the side panels to fit tightly between the top and bottom pieces. Cut all the panels wide enough to create a 3/16-in. lip around the front of the shelving unit. Adhere iron-on edge banding to these pieces.
Fasten the panels with flat-head sheet metal screws after drilling countersink pilot holes through the unit. The unit's frames are hollow, so be careful not to punch through their thin faces when drilling the countersinks. Make sure the screw heads seat flush.