Multiple Dell C-Type Laptops with a WD19TB Dock

I have a WD19TB Dock setup with wireless keyboard and mouse along with two HD 24" monitors, then I plug the USB-C hose into my Company provided laptop and all is good.  Love the setup.   I am in search of a personal laptop and would simply like to use the same setup, but it does not seem like a KVM is necessary since the WD19TB already hosts all the KVM peripherals.   I'm obviously not tech savvy on USB-C protocols, but it seems like a simple USB-C switch is all that is needed -- the WD19TB feeds the switch, and the press of a button switches the dock feed between USB-C connected computers.   The alternative is to just move the USB-C hose from one machine the other, but the point of this post is obviously to avoid that.  KVM type solutions/boxes want to host all the KVM peripherals which seems unnecessary when the WD19TB Dock already does this.