Mate, I really feel for you. You must be feeling very alone and stressed at a time in your life when you should be feeling joy.
Your guy seems to be understanding but does he need to put this pressure on your right now? Do you not have a third option to ask him for some more time, tell him you really want him in your life but you have so much pressure at the moment, and it's not the right time to talk to your wife...???
One thing that you haven't mentioned is how your guy feels about you staying married and having a closed-loop relationship with him? have you had this conversation with him? Is he happy to share you with your wife, if your wife agrees?
I was reading one of your previous posts where you were watching a tv show and your wife asked "do you think this will happen to us?" To me it sounded like she wanted to open up the conversation, she wanted to test the boundaries of your marriage.... did you think that?
Honestly, I think right now if not the right time to have this conversation with your wife. You have a new born, she's probably not sleeping, having to feed every couple of hours, her hormones all over the place etc. You bring up this conversation, she's going to think you want to abandon her when she needs you the most.
If you are going to have this convo, then from my experience and people I have chatted to, your wife needs to know that you are 100% committed to her emotionally, and she is the first priority in your life. When the wife feels insecure, then its a lot of drama and doesn't work.
And take baby steps, instead of saying you want to see this guy on the side, say you want to discuss your sexuality and how she feels about it, or about you exploring it, not sure if these are the right words, only you know.
Please reach out if you need anything, so many of us have gone through similar situations, you don't need to be alone.