Hi Flowertop, it's so hard, isn't it? We all want our lads to be confident and popular, but sometimes they stubbornly refuse to play the game. My own son isn't really shy, but it always takes a while to persuade him to do something new, and he never,ever puts himself forward for anything, eg head boy, prefect etc. I think a lot of them are so afraid of failing that they won't try, and so they don't reach their full potential. Having said that, the more you try to push them the more they'll dig their heels in. We have a thing at the moment about Sea Cadets, my son's gone for over a year and enjoys the boating they do on the river in the summer but hates the drilling. At the beginning of term he said he wanted to jack it in but we agreed he'd go for four more sessions, and if he still felt the same he'd stop. Maybe you could do something similar with your ds, eg say that he should go to 2 or 3 sessions, then you can review how he feels and whether he wants to continue. If he doesn't see it as a long term commitment, perhaps he'll be more amenable.
I was exactly the same as your son when I was growing up and I know my mum was tearing her hair out trying to persuade me to join the kids playing on the street. I was a very shy/lonely child, always with my nose in a book, but it didn't last! Now I'm extremely sociable and talk to everyone & have a wide circle of friends. Being a shy loner as a child doesn't mean you'll be like that for life.
I think you should be gently persistant, but if you make too much of a big deal about it, it could backfire as he'll feel that if he does join in, you'll make a big song and dance about it and that'll put him off.
Not sure if any of this is helpful, but good luck.