Are there any known issues with using a WD15 (K17A001) dock with an HDMI-to-DVI adapter and a KVM switch?

My laptop is a Dell Precision 5520.  The display adapters are nVidia Quadro M1200 and Intel HD Graphics 630.

My current setup is to go from the HDMI port on the laptop to the DVI input port (using an HDMI-to-DVI adapter) on an IOGear GCS1102 KVM switch (DVI is the only option on this switch, which is connected to a Dell E2414H monitor).  This option works, and allows me to use my external monitor with the KVM switch and switch back and forth between my laptop and my desktop.

However, this setup requires that I connect the HDMI cable directly to the laptop.  I would prefer to use a docking station that requires only the single USB-C connection.  To that end, I have a Dell WD15/K17A dock.  If I move the HMDI cable from the laptop to the dock, the laptop no longer detects an external display.  In other respects, the dock is working fine.  Power, ethernet, and USB peripherals (keyboard, mouse, and webcam passed through the KVM switch) have no issues.

Before I do a whole bunch of time-consuming experiments with swapping HDMI for VGA and swapping connections to temporarily remove the KVM between the laptop and the monitor, I'm wondering whether there are known issues with making the WD15 dock work with a DVI connection.