Hard question, this is normally something that a bureau of engineers works on, but I'll try:
> Cost not an issue
In that case, we can omit the recycling part, and use run off the mill tool steel in your specific flavor. Tool steel because it's the middle ground between stainless and carbon steel, so ideal for our purposes. As to how to it's done, we have to look at
>No manpower or time to spare
Full automatisation it is then. There's only so far you can go with that approach in real life, but as you said, when there's no cost problem, we can get crazy. Blade forging, sharpening and finishing can be automated, and with a head engineer for expensive quality control, it should be perfectly fine for your grunts, but assembly is tricky. Luckily, there's a solution for that: child labour! Just let the children, that are too young to fight effectively, assemble guns and knives for you.
Tl;dr: yes, it is, in a perfect world like you described. It is cost intense to maintain a level of quality, but with no limit on cash/resources, it can be done.