The simplest way to do this is to buy displays that can switch between a minimum of two inputs. All you would then need would be the appropriate cables and/or adapters to connect the computers.
Example:
computer A: HDMI output into HDMI input of monitor A, VGA output into VGA input of monitor B
computer B: HDMI output into HDMI input of monitor B, VGA output into VGA input of monitor A
This gives you the added flexibility of having one computer drive both monitors, or having a single display for each computer.
If switchable displays are not practical, there are external A/B switches available for various types of display connectors.
Whatever you do in this regard, the "solution" will likely require modification the next time you get a new computer - different cables/adapters.
You cannot avoid having two display cables for each computer. The only question is whether there's a docking station available that lets you connect the entire computer to the docking station in a single act, with the two display cables running from the docking station to the displays (or display switches). The answer for the MacBook Pro is simple - there is none. If there is one for the Latitude, I wouldn't know.