I would suggest re-cutting the line with a jig saw. This time, clamp a fence to your piece of wood.
Assuming your cut edge is on the right hand side:
First, put the jigsaw on top of the CP piece at its lowest point (the one farthest from true) and mark where the guard ends (the metal piece that protects the blade) on the left. Take a known piece of straight wood and place it so its right side is just on the mark you made. Then take a combination square (or any good known right angle), and align the rest of the straight wood so it's square to the edge of your CP. Clamp both ends, then run your jigsaw down the line, making sure that the edge of the jigsaw's guard stays flush to the fence along the entire cut. This should cut away a sliver from the CP that will leave you with a nice, clean edge.