Wear thick gloves to protect your hands from injury. Grasp a pair of tweezers and pull out the splinters from the edge of the plywood. Lift each splinter carefully and bend it so it snaps. Avoid pulling the splinters in the direction of the plywood, since you could damage the surrounding surface. If the splintered-edged plywood is unfinished, rub a wire brush over the edges to remove splinters instead of using the tweezers.
Rub 150-grit sandpaper over the splintered edge to smooth out the plywood surface, starting from one end of the piece and working your way to the other end. Move your hand in the direction of the grain so you do not splinter the surrounding surface. Continue to rub the damaged edge until you cover the entire length.
Wipe the surface of the plywood with a tack cloth to remove sanding dust residue. Continue to sand the edge of the plywood but extend it beyond the damaged section to blend the damaged section with the rest of the plywood surface. This practice ensures the plywood piece looks uniform.
Wipe the surface with a tack cloth. Depending on the finish on the surrounding plywood surface, leave this edge as it is, or apply a matching coat of touch-up paint or stain over it.