OpenGL GL_SELECT or manual collision detection?

As seen in the image

I draw set of contours (polygons) as GL_LINE_STRIP. Now I want to select curve(polygon) under the mouse to delete,move..etc in 3D .

I am wondering which method to use:

1.use OpenGL picking and selection. ( glRenderMode(GL_SELECT) )

2.use manual collision detection , by using a pick-ray and check whether the ray is inside each polygon.