Great Wall, near Beijing, on National Day holidays

I will be in Beijing October 4 & 5, during National Day festivities. I would love to see the magnificent Great Wall but would like to avoid as much crowds as possible. Which sections of The Great Wall are least crowded? I am a healthy, 57-year old man traveling alone. Which tour companies would you recommend for these sections? I will be staying at a major hotel near Forbidden City. Thank you.