You can accidentally make steel while smelting ore, though it would be more likely to result from the perfect combination of fuel, ore, and air, rather than a single factor like a strong breeze. As smelting takes hours, this sort of situation wouldn't be too difficult to write: an unusually gusty day with irregular winds, an especially good batch of charcoal, ore from a different side of the stream than usual, or maybe you had a local kid take over the bellows for a few hours while you did something else, and can't explain why part of the bloom was different.

Steel, on its own, might not be enough to get you the quality difference you're looking for, though. Pure iron has a hardness of 100-150 HV, which is harder than copper but softer than bronze. Add carbon, and its hardness will increase to around 200 HV (bronze can get up to 300, if you know what you're doing). To get the really high hardness if a modern kitchen knife (around 600 HV), you have to heat the metal and cool it rapidly to transform it into martensite (up to 1000 HV), and then gently reheat it to reduce its brittleness (bringing the hardness down a bit). This is a complex process, and figuring it out accidentally in addition to accidentally making steel is a little bit of a stretch. It seems more likely that your smith would make steel and be pleased that his tools were marginally (50-75%) harder than the rest of the iron he was making.

But there are other ways to get especially good tool iron. If your smith substituted bog iron ore (from a swamp) for his regular supply, he might create iron high in phosphorus. Phosphoric iron can get up to 300 HV (so, 2-3 times harder than pure iron), and it's a much lighter color than plain iron (almost white), so the difference would be easy to spot once it was polished. Phosphoric iron can be hardened by hammering, and doesn't require careful heating and quenching the way carbon steel does. It's more brittle than pure iron, but you can weld strips of it onto a back of normal iron to give a harder edge (really useful for knives) without making the entire blade too brittle. Polish the finished tool, and the hard, white edge would contrast nicely with the duller grey of the tool's body/back.

If you're going to write about a bronze smelter experimenting with iron, you should consider a few other things. Copper and iron are both made by heating crushed ore, but copper can be smelted at a lower temperature than iron, and copper also melts at a lower temperature. Someone used to working with bronze would heat the metal to a liquid and pour it into a mold. This would not be possible with iron. While smelting the iron ore, the furnace wouldn't be able to get hot enough to melt the metal; iron is smelted as a solid, the heavy iron particles falling to the bottom of the furnace and sintering together in a giant lump (which also includes a lot of slag - dirty glass - from the sand that was mixed with the ore (naturally or intentionally; the silicon is necessary to act as a flux, lowering the welding point of the iron particles and helping them sinter together in the furnace). When the iron was removed, it would be a solid blob of molten glass and solid iron, and you'd hammer as much of that slag off as possible before it cooled. You'd then break the bloom up into smaller pieces, reheat them, and hammer and fold them to remove more of the slag. You would never work iron as a liquid - your furnace couldn't get hot enough.

That means that, for your smith, iron and bronze would be two very different materials. Both came from rocks, but one was a liquid shaped by molds, while the other was a solid shaped by hammer blows. Chris Gosden has argued compellingly that this would result in two very different kinds of 'magic' associated with each material; mastery of one would not guarantee skill working the other.

That doesn't invalidate your premise - a bronze smelter would know how to control fires and prepare ore. But he'd have to do a lot more than just throw a different kind of rock in his furnace to get iron. He'd need to build a bigger, hotter furnace, and then learn that iron wants to be shaped while it's glowing hot but still a solid, and that it can't be melted down to a liquid like bronze. He'd have to learn how to draw it out with careful hammer blows to immitate the shapes that liquid bronze will naturally flow to fill. And then he'd have to confront the way that it rusts (though phosphoric iron is more rust resistant - another thing that might make it a good material for inexplicably better tools).