Wrought iron has not been puddled (made) in the USA since 1961. If you can find it, it is wonderful stuff for the blacksmith. One can burn it, but it will take a slightly higher temperature than mild steel before it becomes burnt.
The higher the carbon content, the easier it is to "burn" one's steel in the forge.
If you want to know what "burnt" steel is, ask your friendly blacksmith. I burn my first wrought iron shortly after I made my first and only forge weld in wrought iron. Irretrievable error. Lots of pretty sparks, but a real bad thing to do.
No antigue gun had actual "Steel" hardware, it was either forged wrought iron or malleable cast iron. Colt London revolvers had malleable iron trigger guards and grip frames, regardless of whether anyone's gun book calls them "steel" mountings.
For American flint or percussion hardware, forged mild steel would be just fine, it being a major effort to locate real wrought iron. One must use a flux of some sort, sprinked on the steel, to get it to weld when hammered together. Nature of that flux, and what is a "welding heat" is something best discussed by an experienced blacksmith.