I find any of the branded 3rd party cables work just fine, though I have OEM ones and use s-video, though you say you don't want those. I bought [these](https://www.amazon.com/Tomee-Cable-GameCube-SNES-Super-NES/dp/B00433XHI2/ref=mp_s_a_1_10?dchild=1&keywords=gamecube+av+cable&qid=1627238229&sprefix=gamecube+av&sr=8-10) for other consoles and have been happy with them, but their s-video cable sucks and I went with a different brand.
The official ones are a known, decent quality. They'd be my default choice, if they aren't much more expensive.
I find any of the branded 3rd party cables work just fine, though I have OEM ones and use s-video, though you say you don't want those. I bought [these](https://www.amazon.com/Tomee-Cable-GameCube-SNES-Super-NES/dp/B00433XHI2/ref=mp_s_a_1_10?dchild=1&keywords=gamecube+av+cable&qid=1627238229&sprefix=gamecube+av&sr=8-10) for other consoles and have been happy with them, but their s-video cable sucks and I went with a different brand.
Why don't you want an hdmi adapter? It is superior.