Belial edge, C ID, GH, and HF do not use the Azure. the follow ups on the other hand, do.
Pretty much IF bloodedge were playable it would be odd to make him unique other than all we have is that "When he is in close proximity of the Black Beast his right eye and arm start to work again." meaning the Azure comes back.
I've had this discussion multiple times the GAME PLAN HAS ALL BEEN SOLVED.