Going to go out on a limb and ask why do you think your wireless is fast enough on a monitor and not fast enough on your TV? Most likely what you are seeing is latency on the TV, not the mouse. You most likely need to set the TV to game mode, and even then depending on the brand/model may not be fast enough.
For a wireless mouse I use Logitech M570 and love it, but it might not be for everyone because it is a thumb ball.