A KVM switch is intended to use a single Keyboard, Video connection, and Mouse for 2 or more different computers. The user simply changes the KVM from Computer A to Computer B. And some switches will handle even more computers. The switching process is manual but there are some switches capable of automatically managing the switch.
A Reverse KVM allows two different users (actually workstations is more applicable) to use the same computer from different locations. Each location having its own Keyboard, Video (monitor), and Mouse.
If working at Location 1, the switch is set accordingly. the Location 2 is to be used then the switch is set to Location 2. Location 2 can sometimes be further away and requires longer cables.
So you will need a KVM switch to share the three monitors between the laptop and desktop. And you could also use the KVM to establish a common keyboard and mouse to be used with the chosen computer. Or not use those ports at all.
As I understand your drawings you will first need two video cables to bring in video. One cable for the laptop, one cable for the desktop. Those two cables would be the video "input" to the switch.
The switch would need three video "outputs" - one output for each monitor.
However, if the laptop to HDM/Direct monitor is "permanent" then the switch would only need two video outputs or at least the use of only two video outputs. With, again as I understand the diagrams, the WavLink continuing to be connected with the laptop but before the KVM switch and monitors.
Or if you envision all three monitors being used by either the laptop or desktop then the WavLink would need to be after the KVM switch. Not sure (full disclosure) about that connectivity.
Does the laptop have/use a docking station?
Add plug and port details to your diagram. Consider both inputs and outputs.
Objective being to determine the type of cables (DVI, HDMI, USB) etc. to be used along with genders.
Note: You will need to purchase cable types with the applicable plugs and genders. And cable lengths.
The resulting diagram should establish the physical requirements for the KVM switch.
Google "KVM switch diagrams" to get a sense of how the diagram should look.
You may find some diagram that suggests another idea or option.
For example only (not a recommendation or endorsement):
https://www.startech.com/en-us/server-management/sv231dpddua
Note the drawing and labeling.
Instead of Servers you have Laptop and Desktop.