For the long sides, put the box into the vise and add a piece of wood under the long edge between the ends for support. This gives it added stability when planning and also allows you raise the mid section to plane any hollow areas in the surface. Use the plane on a shallow setting and lift the heel up as you approach the second dovetail at the opposite end. Plane from the opposite end towards the mid section and again lift the heel of the plane, this will avoid it splitting and give you crisp clean corners.
For the short sides, add a scrap piece of wood onto the end and clamp into the vise, this will avoid it splitting on the corners as the piece is too short to plane in from both sides.