Portable Python on the Windows computer. `python -m http.server`. On the Linux computer, something like `wget -mkp` followed by `find … -delete` to get rid of the index files.

(Lots of disks are soldered in nowadays, or the procedure might require multiple M2 slots that the destination mobo might not have. Is your company IT department happy to know their hardware is being disassembled?)

I have not benchmarked to see if this would sustain the 120 Mbps the original scenario would require.

I think sometimes we forget there are plenty of engineers out there whose experience interfacing with a computer begins and ends at the KBM. "Put the HD in the other machine" isn't super obvious to every junior, though I wish it was!