KVM switch for LG G6

Does anyone know if a KVM switch will work to output video to a DP computer monitor? I don't know if they make a KVM switch with a DP connection or not. If they do, can I use my phone along with an HDMI to DP converter? If I get one with HDMI, will a HDMI to DP converter allow me to operate my LG G6 with a USB mouse and keyboard and view it on my computer screen? If so, then how will I plug the DP cable from my tower into the KVM switch?

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