How do you know he's been on dating websites? Do you two actually talk regularly or anything like that? If you don't talk to him face to face when you see him at these walks you do, how often and what is your main source of communication with him? If you want to get over him then remove him from your life and try to forget him? It doesn't sound like he offers you or your life anything positive at this point and you've realised "it wasn't meant to be" so why keep him around?
Also, as a side note, shy people can and do absolutely use dating websites. If anything shy people probably use them more since they might find it harder initiating contact with someone they like irl.