The Idea of Reworking Azir into A form Swapper would be Cool but there Are some points that I feel should be made to more refine your Idea.
I am just going to explain A way to refine the Idea for the first point
What I mean by the first point is that most of the Form Swapper characters have some part of their Kit that makes it necessary for you to change forms. To explain this better lets Separate out the different Types of Form Swappers
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The Best Type in my opinion (so the first I will point out) is the permanent type like Kayn, Kha'zixs, and Kai'sa Where wants you Transform there is really no going back the reason people Transform for this type of Character is because it will buff the Champion and avoiding this buff is Choosing to be a weaker character.
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The Second are unwilling Transformations Like Kled and Gnar where you don't have a choice in your transformations you will at some point Transform. People have no choice with this type of form swap so they are going to form swap
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The final type that I can think of is the Press a button to flip between two forms Like Elise, Nidalee, and Jayce. For this type of form swapper players change between the forms because it flows with the champs Combos. Examples of it would be in the way that Elise's q does Current Health Damage in Human/Mage form and missing Health Damage in Spider/Bruiser form or how Nidalee Triggers bonus damage and effects for her Cougar/Assassin form when landing abilities in her Human/Marksmen form. (Jayce is to complex for my tiny brain so I have no idea what he do)
The Different Damage types as well as how neither form relies on the other makes it pointless to swap forms and ultimately robs the character of an ult and the benefits of a form swap.
A way to remove this problem would be to first change Azir into being entirely an AP champ with little to no AD scalings.
The second part would be to make it where one forms excels in one thing but then loses out on what the other form is good at.
To add some synergy into this new kit I would first start by saying what should he do in each form and why does that form need the other. Using this and the fantasy that Azir was Designed under Could help focus the design more. The two big Concepts of Azirs Current Design and Lore as I see it are Being the King of Shurima that United all the Ascended and the Fact that he is good at attacking and defending towers as well as attacking from behind hes team.
The changes that I would make would be to give Azir A better feeling of summoning his armies forth closer to what Yorick is. A big Reason why I would do this even though it would highly be similar to Yorick, Azir would be an APC/Mage combo and to be honest I highly dislike the lack of control Yorick has over his minions and would like to see a champ where you Decide what your minions do and not some semi-decent AI
Using these concepts I would start by making a small Change to Azirs Passive
Passive:
INNATE: Azir places a marker above the ruins of all destroyed turrets outside the enemy base.
King of Shurima: Azir Can have a limited number of units summoned to the battle field to assist him in his Conquest of the rift
Azir Can summon (3/5/7) units to the battle filed (I would like to add that these are just some numbers that I am making up and would have to be adjusted for Balance)
DISC OF THE SUN: Azir raises the Sun Disc from the selected marked ruins after a brief delay. The Sun Disc functions like a standard turret but gains (15% AP) bonus attack damage. It also grants Azir any Gold gold it earns. The Sun Disc's health decays over 60 seconds and loses 100 armor if Azir dies or moves too far away. Disc of the sun Counts as 3 summoned units while it is active or on cool down.
I would readjust the numbers to make it where the Sun disc is better when Azir is near it and in Ranged form as well as increase the duration a little bit but also increase the Cool down time as well. This would be so that Azir will lose out on attacking power from summoned minions to siege the enemy towers but gain a way to Slow a siege up.
For the Rest of the abilities I just have a Concept and not A full Idea the concepts for the Forms would be while in ranged form you are a Summoner and will prep your forces but will die if caught out where in melee form you are a siege or fighting machine with the main weakness of Azir being AOE Spells that affect all his minions.
For His Ranged form
[Q] would Remain the Same but no hard CC his kit should avoid Hard CC to give him a clear weakness in ranged form
[W] the same but adjusted to fit with passive each sand solider counting as 1 unit and lasting for less time and the soldiers stealing some of your health to make their own like a 3 yours/5 theirs ratio or something I would also make the soldiers single target
Attack: by clicking on an enemy or monster All Soldiers attack one target Then return to Defend Azir if the Target Dies.
or
Defend: by Clicking on an Ally (to Defend the Ally) or the ground to Defend an Area Soldiers will remain within X units of defended target but will target enemies based off of current tower rules
^^^ not for sun disk
[E] The same as above but each soldier while unable to attack will have an increase in defensive stats but be able to be destroyed so that it is not an ult level skill (yes Anivia is a thing)
Part of his Skill expression could be shown here by choosing where to send your Army due to the fact that you are limited to only controlling them in ranged form or if that is not fun by making it where the Ranged form is more about making an army and not really fighting
For His Melee Form I would Set it up to be Azir is Charging in with his Armies to Bolster moral in this form he would once again access to his fancy footwork but would also be risking himself on the battle field.
[Q] Keep to what you say but AP, AP for life
[W] Change into an AS Buff that spreads out between you and the units you rule except sun disk so If you are alone it gives you 100% but with each solider it gives x% less but each solider gets 25% in exchange so you do more damage the bigger the army but you don't have an overwhelming amount of damage
[E] Make into a simple dash no buffs or anything just you go but give it a 2 charge system
TL;DR
Overall I like the Idea of the Rework it just feels like you miss old Aatrox and want to have Azir swap between being Azir and pre-Rework Aatrox
Also this could be an idea for a completely new champ
Couldn't find a Good Shuriman emote so All Hail 
P.S. Sorry for any Grammar or spelling mistakes.
