How is your company's network configured such that you need to physically swap the hard drive in order to connect? What happens if the hard drive dies?
For our VPN details, I would have to get my IT dept involved. My point is that machines often need a lot of additional software and configuration. If the world ran NixOS then perhaps a loan machine with "backups" would be almost as convenient as an SSD swap.
OS X has an incremental, automatic backup system built in called Time Machine, which works pretty well in my experience. You'd just restore your time machine backup to the loaner machine, which would restore the vpn credentials.
Time machine is really a consumer gadget, I'd be surprised if IT departments were deploying it within organisations. Crashplan would be more appropriate, but I'm not sure how smooth the restore would be. IMHO not having a swappable SSD really sucks.
In my experience, Time Machine is rock solid. I've backed up and restored many times onto new machines and the only thing that it doesn't handle well is Homebrew (or anything in /usr/local). I've had the same macOS installation for about ten years now.
Also, in my experience, Crashplan is a steaming pile of garbage. Are you verifying that your restores are checksum-accurate? Are you verifying that all files are present after a restore? Neither was true for me, and support were unable to help.