Yes, the Paul Stallard. Its got lots aimed at therapists, so there might be other books that are more aimed at parents, or children themselves if you search on Amazon for worries or anxiety. But the Stallard has worksheets, so you can turn it into a bit of a project. I think Jacqueline Wilson had a book called the Worry Diary or something - I haven't read it, but that might be interesting? A novel, not a help-book.
I understand about not wanting to medicalise it, or make it into even more of a big deal, but if its not feeling like the books are enough, then your GP should be able to get you a referral to CAMHS (child and adolescent mental health - I know sounds awful, but most people are very nice there!), where someone could help. And CBT is the most common approach for anxiety problems.
Agree with the last posters that you were right to keep giving him reassurance, and also really right to still go out. Another thing to do is pay loads and loads of attention to times when he surprises you and himself with not being worried, or coping really well with a worry (however little the achievement), so instead of thinking mostly about the things he can't do, he gets more aware of the things he can do. I think this is in the book too.
Its sad that he's so worried, but as another poster said, its probably a sign of thoughtfulness, sensitivity and intelligence, and other things to be proud of. I hope he manages to get more control over the worries, and good luck with it all.