MJÖLNIR

Since well before the game was released, I really believed that one of the new weapons that Kratos would end up wielding in the game would be Mjölnir, without any doubt. As it wouldn't be the first time that the Spartan, upon defeating an enemy, would keep the weapon he wielded. And what more iconic weapon of all Norse mythology than Thor's hammer? Yes, you could tell me that Leviathan already works as Mjölnir in the saga, but it's not the same... I even guessed that the third new weapon would be of wind element, as the other two were of ice and fire, it was obvious. So I expected that the "supposed fourth" in discord would be Thor's hammer for being lightning, to round out the elemental and numerical parity of the arsenal.

I find it very curious that Mjölnir is used as a promotional image of the game (with replicas in the collector's edition even), and yet the weapon has no real narrative or playable role in the game. It seems a bit incongruous to me. It's just a popular advertisement. Although I understand at least one of the reasons, because as both the game and the myths are written, Thor should live at least until the end of Ragnarök. So it would be strange to kill him or take away his hammer before the climax.

So, despite everything, Mjölnir being the fourth playable weapon would seem to me a nice gift as a culmination, to enjoy at least in the final stretch of the game. Even if it was only available for the final fights of the story and the endgame.

Roughly speaking, although more forceful and heavier in movements, certainly Mjölnir would be similar to handle than Leviathan. The hammer would be thrown and return to Kratos' hand in a similar way to the axe when pressing the weapon's skill button, but in this case there would be the possibility of doing it the other way around. Holding down said button when the hammer has already been thrown, it is Kratos who moves at high speed (almost instantly) attracted like lightning to Mjölnir (even in the air). So, it would have a wide range of lunge moves and even the possibility of doing aerial attacks combos.
Of course, unlike the other three cutting and stabbing weapons in the arsenal, the hammer is blunt. And, consequently, of demolishing power. So it may not maim your enemies, but it does crush and pulverize their flesh and bones.

Also, slightly unlike Thor's one-handed style, in some moves Kratos will hold the hammer two-handed. Not for its weight or lack of strength but because it is more comfortable to wield it this way due to its large wingspan.
All, of course, with the added elemental variable of lightning, which would mainly temporarily chain stun and paralyze enemies. Besides causing them a lot of damage and having the possibility of pulverizing them without leaving a trace.

Here are an example moveset the hammer might have available:

 THROW AND PULL
(Throwing the hammer horizontally and then holding down the weapon skill button)

AERIAL THROW AND PULL
(Throwing the hammer vertically and then holding down the weapon skill button. Which would also expand Kratos' mobility, allowing him to reach some elevated areas more easily, for example. So most likely this skill would need to be limited with a cooldown)

 LIGHT RUNIC ATTACK

 HEAVY RUNIC ATTACK

 EXECUTION