How to simulate mouse move across different displays?

I have two macs that share an external monitor with a physical KVM. I use Universal Control feature to share the mouse and the keyboard between the macs, if I am on Mac-1 and connected to the external monitor, I can drag the mouse across Mac-1, across the external monitor attached to Mac-1, then the same external monitor instance attached to Mac-2, then across Mac-2.

I don’t use the mouse, I am heavily keyboard user and only use the mouse to move it across Mac-1 to Mac-2 and vice versa.

I want to use BTT to move the mouse across displays but I only find actions to move the mouse across monitors. Is this still a use case possible to achieve with BTT? If yes how so ?

From what I read, I know that the API for Universal Control is not exposed but I am looking to simulate, the fact that I take the mouse, drag it across the displays and have it on the screen of the other mac.

This is a hacky solution but maybe you will find it useful. I made it while copying Amethyst's behaviour to get a full window, desktop/space and monitor keyboard manager with just BetterTouchTool.

Move mouse to right monitor

Move mouse to left monitor