[Help] How can I play games on my TV while still using the steam deck as a controller?

I want to play games like civ that are better played using mouse controls via the touch pads, so I want to use the steam deck as a controller. But the screen is a little too small and some games don't have good ui scaling so I want to be able to play on the TV. What's the best/easiest/cheapest way I can play on the TV while still using the steam deck as a controller? I have a Vizio tv that doesn't support steam link but does support casting. Thanks!