Disabling Connected Monitor

I have two external monitors connected to my MacBook Pro (13-inch, 2019 version). Normally I use all three screens in an extended display arrangement. However, I also have a desktop computer attached to the same two monitors and occasionally want to use one or both displays for that computer. To do so, I want to be able to tell the Mac to NOT use one or both of the two external displays, then use input select on that monitor to switch to the other computer. I want to disable the monitor *without* disconnecting the cables (which is a nuisance, and will also wear out the connectors if I do it too much), and *without* powering off the monitor (since I need it for the other computer).

If I don't do this, then the mouse can get "lost" on the hidden display.

One "trick" I have found to accomplish this is to temporarily set one monitor to mirror another (see https://support.apple.com/en-ca/guide/mac-help/mchl7c7ebe08/mac ; in Displays > Arrangements, alt-drag one display on top of another) but it's a hack.

Is there a better way? I just want to disable the display, e.g. stop the Mac from sending it a signal (which saves power, but also lets the monitor auto-switch to the other computer).