Best option for av cables to hdmi?

I wanted to get a new gaming monitor for my consoles when I noticed it doesn’t have AV input for my GameCube. I was looking online and I read that the AV to HDMI converters weren’t too great because they had input lag. I noticed a composite to HDMI cable and I thought maybe I could use that cable. Would my GameCube display if I set the cable up like this, GameCube–>AV cable–>AV coupler–> Composite to HDMI cable–> TV? If this does not work, what are the best cheap options?