I don't know if NASA themselves could stick Saturn engines onto new rockets, but I reckon the Air Force probably could. Air force technicians are pretty good at fabricating and fitting parts from what I've seen.
Skills like hand fabrication and fitting aren't something that you can store. You can record videos or interview skilled tradesmen as much as you want, but the real skill is something that is learned through experience, it's muscle memory and intuition, not theoretical knowledge.
I worked in aerospace during the transition from Ariane 4 to Ariane 5. The Ariane 4 was a versatile modular launch system and widely considered a successful project. The Ariane 5, on the other hand, was struggling at the time. A large part was because it originally was designed to be a launcher for the Hermes space plane. Hermes was never built, but the design decisions that were made because of it had many negative consequences for the Ariane 5. Most importantly it was not very economic for launching smaller satellites.
It was quite natural to think of enhancing the successful Ariane 4 design instead of building Ariane 5. From the conversations I remember from that time this was not considered a viable path - mostly because the supply chain of the Ariane 4 parts had already gone dry and it was not considered realistic to rebuild them.
For me as a young engineer this was very surprising, but a few years later I understood two things much better:
1. The knowledge to build projects of this scale is very distributed.
There were subcontractors over subcontractors (spread over several
countries) and every one had some tacit knowledge viable for the project.
2. Setup cost for parts production is relevant, even for the small series productions common in aerospace.
While this is I’m sure true, the main point is about knowledge transfer. New people come onto the job, and they need to learn how to do it, and their skill level will always be basically zero. The question is, how do they learn how to do it, reading books or having a mentor watching over them? Certainly having a mentor will make that far easier, but if all the people who knew how to do it are now retired or especially dead, this isn’t possible, and so it becomes considerably more difficult for a new person to learn.
Skills like hand fabrication and fitting aren't something that you can store. You can record videos or interview skilled tradesmen as much as you want, but the real skill is something that is learned through experience, it's muscle memory and intuition, not theoretical knowledge.