That's not what a scalpel looks like... The hole in the blade is where it attaches to a handle, and the blade is therefore disposable, it isn't supposed to be attached at the base.
Also rather than blacksmithing steel without modern techniques for scalpels, obsidian would be a much better material as it is sharper, which is the most important thing for a scalpel.
Also for this kind of time setting the number one danger of surgeries isn't a surgeon botching it, it's infection. Introducing germ theory and sterilization techniques would be far, far more effective at reducing mortality rates. New scalpel designs would have a marginal at best improvement for surgery success rates since this country already has pretty decent technology for blades. Also how is this supposed to even make money? It's not like you have millions of surgeons without access to scalpels.