I always assumed that Fredo's betrayal was common knowledge amongst the Family & the likes of Neri, but Michael wanted to deal with it by himself as much as he could, due to the extreme nature of treachery by an actual family member. Obviously any soldier or capo couldn't kill Fredo Corleone without approval, even if they did happen to find him.
Connie could have known all & still been willing to forgive Fredo, Tom would have been waiting for his Don's orders.

The fact that the Don of the Family wanted to take such a careful & hands-on approach in dealing with this particular traitor emphasised:
- just how serious Fredo's betrayal was;
- how deeply Michael was hurt by it.

I don't think there's much else in the detail.