I vote for trimming. I think it will look lovely.
Another easy way of making the block would be applique: cut a large circle and a large square. Fold the square in half, then in half again, and press the center fold. Do the same thing with the circle. Open both pieces out flat, then stick a pin through the center of the circle, right in the intersection you just pressed. Then stick the same pin (with the circle still on it) in the center intersection of the square, push the circle down the pin onto the square, then buttonhole stitch or zigzag around the edge of the circle. Turn the block over and cut away the square background that is behind the circle. You should now have a circle appliqued onto a square. Now cut the block into quarters and voila, 4 Drunkard Path blocks.