Niklas,
Unfortunately, the writers talking about damascus barrels often neglect to cite sources for Swedish iron when they mention it.
Puraye is talking about the early 1800's when he writes about the horse shoe nails. There are a lot of references in the English literature to using of horse shoe nails for making twist barrels. When tracking those references I finally found a steel/iron price sheet. The English were purchasing the nails directly from the mill because of the low cost. I believe this was a common practice from country to country.
There is a disagreement between Puraye and Gaier about overcoming the problems of coke smelted iron. Puraye, quoting Heuse-Limone in 1884 says they tried Swedish iron but had problems during etching. Apparently they could not produce strong patterns and preferred iron from "Mineur et fils of Couver" for damascus work. I have to ask myself if Heuse-Limone is being totally open and honest here. He knows the French and English will be reading this.
Gaier simply states that the barrel makers became obsessed with finding charcoal smelted iron and turned to Swedish iron for a solution. He also states they kept seeking sources for the product.
My take is that both are talking about late 1800's. At this point in time, the barrel makers will use any charcoal smelted iron they can find that will meet their price point. Puraye says that they simple brushed on sulphuric acid to bring out the pattern. I have spoken to Dale Edmonds about this. While the pattern will appear, it will not last. He thinks it was done to check the quality of the damascus work. If found suitable then a better etching method would be used.
You can find Gaier in English, but expensive. He wrote 4 Centuries early on with 5 Centuries being a later update. The English versions are not the best translations. Puraye translated a small portion of his work and published in the American Rifleman, April 1976 & May 1976. I have promised myself to translate all of "Le Damas" this year. When it is finished, I will post here and make it available.
Sasche has reproduced damascus barrels. I do not recall if he discussed the smelting of the iron or not. I will have to check.
We are all still learning here...
Pete