While his suitability for this role was indeed in question, it's not impossible that Thor could have handled it anyway. The snap may very well have had a longer-lasting impact on his wellbeing than it did on Smart Hulk, but he was still the God of Thunder.
If Thor had the gauntlet and did the “snap” I would be less worried about what would happen to him and more worried about what the outcome of the “snap” would actually be. He would probably survive the snap, and might be pretty hurt, but mentally I wouldn't trust him doing it at all.
Even so, it seems unlikely that Thor would have been incapable of using the Gauntlet. In Infinity War, he endured the power of a star to forge Stormbreaker and came out with no significant injury that could hinder him.
Let's say Iron Man handover the stones to Thor after getting them from the gauntlet. With god power, Thor will be powerful to handle the stone's power, and he can survive the snap with some minor damage to the hand. Since Thor snapped instead of Iron Man, Tony still be alive and the funeral won't happen.
Post-snap, Thor had the same 50/50 shot at survival as everyone else did. The fact that he was left alive was either luck (because Stormbreaker will come in handy) or by design, since the original Avengers were all left alive.
Note that all the members of the original Avengers team — Iron Man, Captain America, Thor, Hulk, Black Widow and Hawkeye — survived Thanos' attack.
Characters who survived the snap.
It's worth noting that the original "Avengers" group — Tony Stark, the Hulk, Thor, Captain America, Hawkeye, and Black Widow all survived. Trailers have shown Hawkeye donning his new Ronin outfit.
There are very few powers that Mjolnir grants him, but it does seem to amplify his connection to the Odinforce at all times, and accordingly, powers him up. Still, most of Thor's powers can be performed without Mjolnir. Depending on the iteration, though, Mjolnir can disguise Thor as a mortal.
Thor's confidence was only shattered when he failed to aim for Thanos' head and allowed the Mad Titan to Snap his way to victory. Thor drank through his five years of depression and he allowed his physique to deteriorate, but his mental health was in equal distress.
Remember in The Avengers Tony pretty much sacrificed himself by carrying the nuke through the wormhole, yet in Avengers: Age of Ultron he was not able to lift Mjolnir. So, Tony simply risking giving up his life by performing the Snap isn't necessarily enough to deem him worthy.
The winner of this fight would be Thanos based on his superior brute strength, and raw powers. However, if Thor uses some clever strategies, he could defeat the villain, especially since he has access to more powerful weapons and techniques.
This is why the hammer ends up being treated almost like a child of divorce at the beginning of Love and Thunder. It chose Jane because of Thor's request, and doesn't return to him when he asks it to. He gets frustrated with this, and this ultimately makes his relationship with Stormbreaker a bit rocky.
All in all said, Thor was a whole can defeat Hulk. A large part of that is being able to wield Mjolnir. Hulk cannot keep up with or match Thor when fighting with this might weapon. Hulk struggled to defeat in The Mighty Thor #385 even when using three of Thor's weaknesses against him.
Tony Stark snapped the supervillain Thanos and his army out of existence and died himself because of the irreversible damage inflicted on his body due to the toll of using all the the Infinity Stones at the same time.
If Thanos is powerful enough and worthy enough to bring the Infinity Stones together when no one else in the history of the cosmos ever could, then perhaps he would really be worthy of lifting the hammer without the Gauntlet.
How much can Thor lift at his base form? - Quora Answer (1 of 4): Infinite weight. He was able to lift a book which had infinite pages when he was a kid. Yeah, he did that when he was just a freaking kid. Both Odin and Bor failed to do so, yet Thor was casually able to lift the book and its infinite p...
Thor, son of Gods, has enhanced longevity, augmented by the Golden Apples of Idunn. He also possesses superhuman strength, speed, agility, durability and immunity to most diseases.
He's the second strongest Avenger. He is the mightiest. He was able to lift a planet, knock Thanos back yards with one punch, hold back the Hulk with one hand, nearly killed the Beyonder with just his brute strength, etc. Godlike speed: Thor can move beyond warp speed.
Other than Thor and Odin, certain other individuals have proven worthy of lifting Mjolnir in the primary continuity: Roger "Red" Norvell (a deliberate ruse by Odin) Beta Ray Bill. Buri (also known as Tiwaz, Thor's great-grandfather)
The reason why Yelena is one of the missing MCU heroes in Avengers: Endgame's finale, though, is because no one really knew about her. Black Widow (Natasha Romanoff) was dead by this point, and while Hawkeye (Jeremy Renner) knew of her, they had never met or been in contact at this point.
DC & Marvel's Crossover Universe Made Hulk the Weakest Avenger - IMDb. The Hulk has been called the strongest Avenger given his unparalleled, planet-shattering strength, but within the 2099 future of Marvel and DC's crossover universe, the Hulk would be considered the weakest Avenger (for one specific reason).