Alignment Usually Isn't Hard To Determine
Alignment often isn't that hard to figure out anyway. Spells that can detect it are readily available, some classes (like Paladins) can detect evil as much as they want, and in certain cases you can discern it from their actions (a Cleric casting a Good spell can't be evil, because a Good type spell can't be cast by Evil Clerics).
It's possible to take steps to conceal it, but in my experience not many people do that.
So I don't think the real risk here is that you're going to make alignment too easy to determine.
Overemphasizing Alignment
To me, the biggest concern is that by having the world reflect alignment so readily, you're making it more important. Being Good is so important in your world that all magic is affected by it, even when the spell is thematically neutral and doesn't do anything that relates to alignment.
You've elevated alignment to be a more prominent thing. Considering how rigid the alignment system can be and the problems it can cause with player behavior, that's not something I would want to do.
Consider what that means? Normally if I see someone cast a Fireball to take out some creatures, I'd just determine what to think about that based on what I saw, and if I cared about those creatures or not. But now I'm seeing an Evil Fireball. If I'm a Good character, do I have to do something about the evil spellcaster? What if they're on my side? What if the people they're attacking are also evil, but those people are using weapons so I can't tell?
The alignment is so in my face that it distracts from trying to figure out the motivations of the people involved, because literally the first thing you've told me is "that Wizard is evil."
"Sentient magic items function as NPCs under the DM's control," says the DMG (214). They have their own personalities; they have Intelligence, Wisdom, and Charisma scores. If they weren't trapped inside swords and boots, they'd be out living their lives and making decisions just like everybody else.
The PHB (122) says celestials and fiends are locked into their alignment, but "for many thinking creatures, alignment is a moral choice." Even the races created by evil gods have free will, and can pursue good alignments if they choose.
I gather that HotDQ isn't very specific about Hazirawn's personality, but if there really is a sentient being in there, you should be able to change its alignment the same way you'd convince a wrathful orc or bloodthirsty gnoll to turn toward Good. It could be a philosophical argument, or a series of object lessons that show the sword the error of its ways. Your chances of success would depend on Hazirawn's own force of personality, which is why I brought up that Charisma score.
Although RAW implies that people can change their alignment, it's up to your DM whether they actually can, and whether an outside agent can impose that kind of change. In any case, my answer is that a sentient magic item, by virtue of possessing a personality, should be treated like a person.
(If you can't hack the philosophical argument angle, you might try to get Hazirawn to draw Balance from the Deck of Many Things...)
Best Answer
Yes.
In the original Forgotten Realms setting, the supplement Old Empires by Scott Bennie detailed the realms of Mulhorand, Unther, and Chessentea. The Untheric pantheon, in particular, was ruled by Gilgeam:
Gilgeam's alignment in stats blocks is given as Lawful Evil, but the text described above makes it clear that this was not always the case, unless one can reconcile "just ruler" with a lawful evil alignment. Further, it is quite clear from the text of the book that Gilgeam was not simply a mortal proclaimed as god-king, but a god (indeed, the chief of pantheon) in his own right, with defined major and minor spheres and leveled clerics described in the supplement.