Is there a cable for MacBook Pro that functions like a docking station over USB-C connector?
I think the word you are looking for is docking station.

Otherwise, if you have a spare laptop and the meetings are within the same building or VPN-enabled (i.e. on the same network as your MBP), you could just use the native OS X VNC server/client by enabling remote administration (or whatnot) in System Preferences.  Then just leave your MBP hooked up, and on the remote machine, open a Finder window, hit Cmd+k, and type vnc://ip.or.hostname.of.your.mbp, and hit enter.

Alternately, if your company doesn't frown on it, you could use TeamViewer for remote access over the Internet.  It has built-in proxy support if you require that, as well.

If your spare is a Windows laptop, you can install xRDP for OS X, and use Microsoft's Remote Desktop Protocol to remote into your MBP.  I prefer RDP over VNC any day and use it almost exclusively on all of my *NIX machines.