Eddie was a class act. He couldn't live with his betrayal to Nucky, but I really think that if he'd fessed up to what had happened Nucky would have been sore initially, but would have figured a way out of it. I certainly don't think Nucky would have offed Eddie because he recognizes Eddie's loyalty and devotion through thick and thin.
On another level I also see Nucky and Chalky being tight. I wonder if Narcisse understands that by going after Chalky he's also going to have to deal with Nucky.