Hi S.!
My daughter did not walk until she was 16 months old. She was 11 months old before she crawled. She was just like your son...perfectly content to do her own thing. The doctor told me not to worry about it. The doc said that there was no time table to worry about unless she got past 2 years old and wasn't walking.
So, my mom and I taught her to walk one weekend. My daughter LOVES her Nana AND she loves to play with a ball. So, my mom got about 3 feet from me and held my daughter's favorite ball. I would balance her and start her walking, then ease my finger out of her hand. If she wanted her Nana and her ball, she had to get there. It didn't take her long to toddle over to my mom and the ball. Gradually my mom would move father away from me. We just kept at it several times all weekend and by the time my mom left, my daughter was walking. Don't know if any of this helps, but it might be worth a try.
By the way -- I used to get SEVERE judgement from other moms on my daughter's slow development. I was told I wasn't doing good enough and my daughter received negative attention because of her slow development. She is now a very active and bright 4 year old. Her preschool teachers tell me all the time that she is one of the most advanced in her class. I always said that my daughter did things in her own time and in her own way. Maybe your child is this way, too.
Take care,
S. A.