On the ship, Thanos with just 1 stone and the Black order have wrecked Thor offscreen even though the likes of Valkyrie, Heimdall, Korg, Loki, Hulk and a bunch of Asgardians are on there. When Thor tries to fight again he gets brushed away easily.
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And when hes talking with the Guardians about going to Knowhere to stop Thanos getting the reality stone Thor says hes already too dangerous when he just has 2 stones. I dont think it makes sense to say that getting the weapon would just improve his chances as delaying confronting Thanos to get the weapon means he is free to go round picking up more stones and is ultimately the reason why he is able to do the snap. If there was any chance that Thor along with the Guardians could have stopped him on Knowhere that woud definitely have been the right thing to do.
Also look at the language from Thor:
Gamora: Hell be too powerful to stop
Thor: He already is (with just 2 stones)
Thor: Im gonna hold it open
Eitri: Thats
suicide
Thor:
So is facing Thanos without that axe
Thor is saying he is absolutely no match for Thanos without Stormbreaker and there is no shame in that as the guy just decimated Ragnarok Hulk to the point of being too scared to come out. The words are pretty clear. Stormbreaker though elevates him to a whole new level.
