Edgar Ætheling for King - the Normans aren't going to risk a second invasion as the King of France, Philip I and his mother who is acting as regent, is going to take full advantage of the death William and invade.
The thing is that if the Normans have WON Hastings they won't need to re-invade as they will already be here. One assumes that William left a regent at home in Normandy ? But I can't off the top of my head remember the ages of his children at this point in time ? Now, if the Normans have been victorious but William is dead, its a very confusing situation
I agree that all and sundry will leap on Normandy and try to tear it apart, but remember that it took an age to get a clear run across the Channel, so the Norman army won't simply be able to re-embark and go home quickly.
Thus, victorious but worried about home, its in a strange position. It has the field and has the potential to intervene decisively in English affairs, but it needs to get home, or at least a large part does...
I would think therefore a negotiated settlement with Edgar and the Witan, followed by re-embarcation to try to save Normandy. BUT this does not end the scenario as others, like the Count of Boulogne, will try to take advantage of England's weakness and advance their own plans