Some converters are hard wired to the 120v breaker, while others are plugged into a receptacle, which in turn is on a 120v breaker.
So if the one breaker is doing both converter and TV receptacle, that might mean all you have to do is unplug the converter and leave the receptacles' breaker on.
If hard wired, as others said, just move the black wire from the converter over to a different breaker not needed and share with that, or even add a breaker if there is room on the bus.
If hard wired , you can also as said, insert a switch on the black wire from the converter before it gets to the breaker.