He's not gonna want the letters. If they are meaningful to you keep them. Don't go through them unless you're looking for a big cry. Just put them away. At some time in the future you may want them. If you give them to him he'll throw them away or leave them behind (even though he might possibly want them in the future). No WAS on here that I can remember ever actually wanted those things at this point. Put them up in your closet out of sight for now. Take down the wedding photos if you have them and replace them with something cheery about adventures. This is a good opportunity to signal that you are dropping the rope, moving forward. It may unsettle him to see you're not pining away, and that can be good. You're right to remind yourself he's seeing an OW right now.
I still have letters my ex wrote me when we were dating - I haven't read them since before my divorce. They're stored up in a closet somewhere. My kids might find them interesting decades from now. Right now they'd still be an open wound even though we've been divorced 11 years. Actually, now I'm kind of curious to read them and see if the early red flags of his narcissism are there and I just missed them?