And no, no one needs 4k where a KVM belongs (which is in a server room).
Everything I tried was garbage:
http://penguindreams.org/blog/4k-uhd-kvm-switches-the-starte...
There are a few in the $500+ range I have not tried, but you are wrong, there are use cases for 4k switching. I mean, do you really want to have two 4k monitors next to each other when you could just have one for half the cost?
I have often wondered why no one offers wireless keyboard/mouse combos with multiple USB fobs and a switch on the keyboard to change which fob it talks to.
Your setup is rather peculiar, and wastes a computer. It is usually done with dual-booting or virtualization, while multiple inputs (which I bet your screen has) or HDMI switch could handle it as well (although without handling keyboard/mouse).
KVM's were designed for server environments, sold to server environments, and only take server environments into consideration where VGA+USB will remain the status quo for years to come.
If you're really set on a KVM, take a 4k-capable standalone HDMI switch, a USB "switch" (https://www.amazon.com/IOGEAR-Computer-Peripheral-Sharing-GU..., or a USB KVM), and an arduino to strap it together as a unit. Unless servers do away with VGA (hahah, no), I doubt you'll find a product for an affordable price that does what you want.