If he's kept the notes, etc. to protect from legal stuff, it sounds like he's put that behind him. Besides, just looking alike does not guarantee paternity.
My view is that biology doesn't make a parent. If this child is 4, and already has a dad, to swoop in to his life now would be incredibly disruptive. It would be disruptive even if he doesn't have a dad. And...your husband may be a wonderful father, but clearly the other woman does not want him in her/their life after all this time of no contact. To force her to do so would also bring another layer of chaos to this child's life.
The notion that he's missing out on something assumes that he's missing anything at all. And whether she's the model parent or not is irrelevant. There are lots of so-so parents out there; we don't just jump in and 'help' each of them with our wonderful parenting skills. This woman made it clear that she doesn't want him in their lives, and he made a pretty clear statement by not going to family court to push the issue (which he could have easily done). His is not, at the end of the day, that child's father, regardless of what the DNA may say.
I think you'd do best to leave well enough alone. You're playing with a child's emotional safety and well-being, and while you're doing it for good reasons (wanting to share a wonderful father with him) the likely drawbacks will outweight the benefits.
And, I think you should spend some time thinking about why you've carried this obsession with you so long.