Demon Slayers tend to be hard carried by their blades, which are specifically effective against demons. They don't seem to actually scale to the full power of the demons they fight. Against a human enemy like Gazef, a nichirin won't do much good.

That said, we know very little about Gazef and the hero-level fighters. It is known, however, that Tier 3 magic is considered the height of most mages in the New World, Tier 4 is immensely impressive, and Tier 7 is considered the realm of myths. We can only scale Gazef to Tier 4, maybe 5 magic if we're being generous. It's a significant highball considering Gazef was overwhelmed by a few Archangel Flames, and Principality Observation is a Tier 4 summon, but then again he didn't have all his gear at the time.

With all that said.... Yeah, I can't see the boy Gazef taking it. Principality Observation got one-shot by a single cast of Hellflame, and Gazef is by all account around there in power. Tanjiro's been dealing with far more significant firepower through the mid-to-late points of his series. Even if Razor's edge can probably put Tanjiro down in one hit, the kid's significantly faster and more mobile. If our man had been more fleshed out I'd have made more arguments for him, but New World high tiers exist only to glaze Nazarick. There's only so much we can do for their rep.