Even though we are talking about laptops, which by definition are moveable, you should not move them unless you absolutely have to. Ergonomics is a very good reason, and it avoids cable entanglement.
I assume every laptop you move only uses 1 screen? Any KVM switch that supports HDMI and a extra screen might be helpful. As most laptops have a HDMI output connector to support a second screen, you could use those outputs in combination with the the KVM switch which you connect to to the extra screen.
Whatever content you need to check on each laptop, if you move that to the second screen on each laptop, you can now easily check on the extra screen. That will reduce your need to move laptops to practically zero. However, KVM switches are not cheap and often also reduce the refresh rate of the screen output. Granted, not such a big issue, unless you have gaming laptops (with 4K screens and 120Hz refresh rate or higher). And there is a need for a separate screen, which requires desk space and solutions for that are heavily depending on your setup. Such solutions may cost a significant sum as well.
But what Target says: much more detail is needed for better answers than the generic ones you are getting till now.