Sophie,
You two are done after a year. Move on. That was the past. You have broken contact with him.
My take on past relationships is to learn what was my part in it. I see all relationships as a learning opportunity about how I am/was. What made me choose her? What was in me that made me want to be the boyfriend? What made us incompatible? What was my part in the breakup? What areas of growth are for me?
Sophie, why is it important for you to absolutely know whether or not he cheated on you or not? Would your shame be any less? I would work on not going into your shame place instead.
There is a TED talk by Bene’ Brown about shame. There is a video of her talking with Oprah as well on shame.
Mark