Wong and Strange both said that their order protected the time stone. Tony had a phone to call on Steve, Wanda, etc. I mean, they were still on earth
I mean, simply because I don't know where the Prime Minister of Canada is at this right second doesn't mean he's ceased to exist.
More than that, Tony had Friday, all his suits of armor and probably that Edith thing back on earth. And on top of that, he knows that simply taking the time stone from earth won't be enough to protect it, because Thanos is after the mind stone as well, also on earth.
That's more than what Tony had
And Tony knew that if he failed, Thanos would come straight to earth. Even if he didn't know the details of the Snap plan, he knew from Bruce what Thanos was about. And that he's beaten two of the strongest Avengers.
IMO, Tony plowed ahead just to get it over with, without regard for how they might actually win.
Also remember, the only things that Tony knows about Thanos were told to him maybe a few hours ago by Bruce. And we don't even know if Bruce told him that Thanos kicked the Hulk's ass. So he may have thought Thanos's power was in his armies, and that between him, Iron Spider, and Strange, they had a chance of beating him on their own.
Wong and Strange did say their order protected the Time Stone, but Tony has no way of knowing how big that order is. And even then, he really didn't get a chance to see exactly what they were capable of. The fight against the Maw and the big guy was rather short, and Tony spent most of it separated from the Wizards.
And I don't think he had Edith at this point. I feel like Edith was something that maybe he built in those five years between the movies, to protect the Earth in case any other hostile aliens decided to show up.
He didn't have Friday. Right after he gets on the ship and he's talking to Pepper, he looses the call. Friday tells him something to the effect of "I'm loosing her, Sir. And you're loosing me, too." at which point, her audio fades out and we don't hear from her again. I think the AI his suits interacted with was on an Earth-bound server, and once they were in space he lost connection with it. So while he could still operate his suit, he no longer had the AI feeding him information. That's why he couldn't connect to the ship (even if it could connect to an alien network), and why he and Peter had to try and steer the ship manually.
He knew that Thanos had the power stone and space stone, and had killed Thor ("Thor's gone.") He had no reason to think that he could stand a chance against Thanos. He really had no reason to think that Thanos would approach alone
He had a guy with the time stone. They could have worked it out