HDMI switcher

Hi there, im thinking of buying the X1 remote and have the following questions. My set up is Sony HT A9 connected via HDMI Arc, with the following devices connected with a HDMI switcher, which you have to press a button to move to HDMI source1, 2 & 3. Sources are, SKY Q, Dune 8k Pro media player and Apple TV. Does the remote work with the 3 way HDMI switcher I currently have. The Sony sound system, is connected via Arc to AWOL Vision 2500 projector. Can the remote also work correctly with, SKY Q, AWOL Vision and the Dune media player. TIA