I do something along those lines.
The laptop in question is an Acer Nitro 5 (older model), with an internal M.2 and SATA connector running OpenSUSE Leap 15.2.
The system is set to boot from the SATA connector. It has a SATA extension cable connected, with the end hanging out the side of the laptop for easy access. eg:
https://www.ebay.com/itm/15-7-Pin-SATA-HDD-Extension-Cable-D...
<-- I don't know the seller at all
The laptop itself is setup and "ready to go" (eg external monitor, keyboard, mouse plugged in), and doesn't get moved. All it needs is the appropriate SATA drive to be connected then powered on.
Been using it this way, swapping over drives as needed (while powered off of course) for a few months now. Works perfectly.
This kind of setup would probably work ok for you if you're using Linux, as most distributions include the common hardware drivers. So even differences in hardware between the laptops (within reason) generally won't be a problem.
If you're using Windows though, no idea. Even with identical laptops in all locations it'll probably notice different serial numbers on devices. Not sure how that would play out.