It's been more than a year and I still think about this part! I guess by a mind of someone from LWM says that if this happens, the most logical move was to make the friendly fire worth it, and KILL the Duke for good. That way, at least the good sister's death would not be meaningless, and Elsa wouldn't be having him to worry about in the future.
Normally I'd favor Disney not showing an on-screen death scene, with blood and all. But in this case... ach. The Duke needs to die. He's not a respectable villain - he's a weasel, a coward, and a jerk. And personally, the only character I hate more than a villain is a jerk. In the first Frozen movie all he received was banishment, and how long exactly since the last time Disney actually stabbed someone to death with an ice spike? As long as he lives he's like a threat - like Grima Wormtongue to King Theoden.
Personally, I'd give him an old-fashioned stab death: on-screen, close-up, using an ice spike from Elsa. But not by Elsa's hand... a male. handsome, stoic, stern, similar and different from Elsa, who's got powers of Nature - wields power of Time.