I want to run this, I have a physical copy of the game and a working Wii but I don't know how to screen record television, can you help me out?

Unfortunly, unless you have a capture card, recording console footage might be a challenge. As long as your gameplay footage is legible, you can just film the television screen with a camera.

Emulating is also an option assuming that your computer is capable of running the game.

My computer is a GTX1650 so it should be able to run it. I don't like emulating things because I kinda feel like that counts as piracy? I'd much rather play it with the Wii Remote as I'm used to. Thankyou! If I record it then it will be when noone's in the house, which may take a while to happen.

That's understandable.

If you ever want to change your mind, you can always use CleanRip or USBLoaderGX to dump your copy onto a storage device such as a USB or SD card and pair the Wii Remote to the computer if it's compatible with bluetooth.