We are having our first baby soon, so I don’t have any experience with this yet, but it might not be helpful to suggest he use techniques from speech therapy. Just because they have worked for him doesn’t mean that they will work under all circumstances. And maybe if he’s having a really hard time right now he can do things that won’t require talking with the baby. I know that reading aloud is an extremely hard situation for my husband (probably the thing that makes him stutter the most). He has a lot of anxiety about reading aloud to our child. But he could always listen to audiobooks with the baby if he finds reading aloud too difficult. A walk might feel overwhelming because if you are out with a baby it’s pretty common for people to stop and chat, and maybe your husband doesn’t feel up to that. If he’s totally withdrawing it seems likely he might be depressed, though, and that is a separate issue.