I have a third monitor with speakers, connected via HDMI, which I would like to use to see and LISTEN at the same time my audio productions for video, inside Sonar.
However in Sonar, my Driver Mode is ASIO (Scarlett Solo) which does not allow me to use the monitor speakers via HDMI, once ASIO is routing the audio to Scarlett Solo audio interface.
I wonder if is there any way, without leaving Sonar, to easily (and temporarily) route the current ASIO output to another Windows Sound Device without messing with Sonar preferences?

Windows doesn't handle ASIO at all. Windows use MME, WDM/KS.

There is a 3rd party app called Voicemeeter (Google it) that can do amazing things with routing audio between different apps and using ASIO at the same time. It's donation ware so up to you how and if you contribute.

Buy a switch for your two phono outputs. Two cables out of that,one into the TV. Won't be HDMI though.