"I wouldn't trust the hardware if it's that old, though."
Exactly which is why I would get new hard, do a nice clean install - put in your config, swap them this provides for very short down time. How ever long it takes to you swap the cables really. And if something not working because you missed a config, etc. Then you could swap the cables back.
To me this is the safest approach since swapping disks maybe something else fails on the ancient hardware on a reboot. Shit does that old of hardware even support sata as a disk connection.. You mention soekris, what model number - prob has some soldered CF so can not even swap that.. I would prob go with their net6501-70 if customer wants to stay with same namebrand, etc.
But for that price point why not just go with pfsense sg-4860 or Netgate RCC-VE 4860, etc.. Sure that would huge improvement to some soekris system from 9 years ago ;)