You can get a physical HDMI button so you don't even have to unplug anything: https://www.amazon.com/gp/product/B01L8LLP2G/
The issue is 4k@60.
Not full emulation and remaining "connected" - just the ability to press a button and change what the device is plugged into.
Edit: the only ones I could find with usb c were full KVMs and far more expensive. I would guess a female usb c to male usb 3 adapter might be a cheap workaround.