For concealing the edges of plywood to give a clean solid wood appearance, cabinet makers choose edge tape. It adheres in seconds thanks to the heat-sensitive glue that's on the backside of edge banding tape. Just heat up a household iron, and use it to press the edge tape onto the edges, the glue melts and then dries in a moment.
 
Available in a variety of popular woods and in several sizes: 25' or 250' rolls, and 7/8" or 2" widths.