Question about Lenovo ThinkPad Hybrid

Hello everyone, I have a quick question: I use this docking station at home for home office. I have connected my two screens, mouse/keyboard and webcam to it. I used to have an Aten switch in between so that I could switch the screen and USB devices between my office laptop and home desktop at the touch of a button. But since I have a second screen, this doesn't work: the Aten switch only supports 1 HDMI device. I therefore currently use the Lenovo docking station when I switch between desktop and laptop, i.e. I simply plug the docking station into a USB-A port on the desktop and both screens and keyboard/mouse are then connected there. This works quite well, but it would be mega cool if it could be done without having to plug it in, i.e. with a switch that I can operate at the touch of a button. I would therefore need 1 x port for the docking station (USB-C) as well as 1 port USB-C (laptop) and 1 port USB-A (desktop) as counterparts. Is there such a thing?