No problems. There are alternatives like a straight PS2 to HDMI cable (https://www.amazon.com/Hyperkin-HDTV-Cable-PS2-playstation-2/dp/B07NSTDKHD).
You could always look for the official PS3 component cable(https://www.amazon.com/Sony-V-Component-Cable-PS3/dp/B000L35Z8I). These will usually be more expensive because they are rare Sony products that aren't made anymore. But because the PS3 has the same AV port like the PS2 people have used it no problems.
There is those cheap HDMI converters which I got and absolutely do not recommend! There is a better one that reviews better (https://www.amazon.com/Playstation-Console-Adapter-Improved-Converter/dp/B07MYVF61Y).