There are no rules about who to grant to sensitive magic objects in particular, so the normal rules apply. If the element does not say that only a specific alignment can / can not match it, then any alignment can be granted.
An example of this (as stated in the Medix2 response) is the Moonblade, which says:
(Requires the harmonization of an elf or half-elf of good neutral alignment)
Hazirawn does not contain any indication suggesting any limitation of alignment, so any alignment may adapt to it.
When the user is in conflict with the item, the item can make requests
Now, since what happens when a user with a conflicting alignment agrees with him, the rules for sensitive magic objects come into some details:
A sensitive object has its own will, shaped by its personality and alignment. If its wearer acts in a manner contrary to the alignment or purpose of the article, a conflict may arise. When such a conflict occurs, the object performs a charisma check disputed by the charisma check of the wearer. If the article wins the competition, it formulates one or more of the following applications (omitted list)
Therefore, even if they are not explicitly limited to alignment conflicts, it seems quite likely that a user with a weapon opposed to their alignment would conflict with the particular purpose of that weapon (if they at a given time and the rules describe how to fix it (up to the element taking control of the user).
The Dragon Queen's treasure does not note any particular Hazirawn goals or behavior, but a deputy minister can (and probably would) suggest some things to make it interesting.