Amazon has a lot of cheap KVMs now. I have a DisplayPort one with 3 USB ports and my favorite part, a wired button to switch between computers! I just stuck the button to the bottom of my desk top and can switch instantly. There’s also a wireless remote I’ve never tried and a keyboard hotkey (though using its special keyboard port confused my Mac so I plug my keyboard into a hub through the KVM’s ‘generic’ USB port.
I’m not affiliated with the maker in any way but if anyone’s curious I can go look up which one I have. It was just a random Chinese thing under ~$45 or so.
As far as I understand it, everyone is better off completely avoiding HDMI in favor of DisplayPort if at all possible.* HDMI has many confusing poorly-specified versions, includes a bunch of DRM to serve content cartels rather than the consumer, and just overall is less reliable. Is going to DP an option for you? Hopefully you have DP as an option on both ends of everything.
My Amazon cheap DP KVM is fast enough for me when switching, my guess is somewhere in the 0.75-2 second range, I'll have to time it for you. I'll reply again with the results.
*Note: i mean for monitors, i'm aware that i'm not gonna avoid it in the living room :)
I tested it. It's about 3 seconds when switching to my Mac Mini (where this is the one and only monitor) -- it takes a couple of seconds longer to switch back to my laptop because I use the laptop open and macOS seems to take forever to think about which windows to move around randomly before lighting up the external display.