The difference I see with Esdeath is that her power's always been about freezing external things. Her imperial arms was always a damage-dealing type like Mine's, while Tatsumi's and Leone's have been user-stat-increase types that give the individual a boost. Never has its power manifested outside of its user.

It's possible I suppose, given the nature of this adaptation. Transferring her Imperial Arms to him would seem more plausible however.