i havent had a problem with not using coping but if i was going to use it i would def just use some like 1 inch or 3/4 inch pvc on the side and have it slightly higher then the hdpe since your ski flexes down it will keep the pressure off of the edges of the hdpe but you ski on the meat of the plastic in the middle of the box
yeah i made a big butter box, covered it with hdpe, and never used coping. I've never caught an edge on it, and it's really easy to learn sw ups, nose and tail presses, and 270 ons. i would try your box without coping before you put some on.