It so happens that there is a software only way to do this.
I was watching LinusTechTips and they were advertising this software on their end of video sponsor.
The software is called Synergy.
It actually works by creating some sort of local network and communicating over your own computers, making the experience very, very fast. The benefits of this over a hardware KVM switch is that this software is as low as $19, depending on the option you pick.
The $19 option would be perfectly suitable for your needs, other options are encryption over the network, and unless your network is already insecure, you dont really need it.
Hope this is a suitable suggestion for you.