Honestly, you shouldn't have anything to worry about. As long as you have an analog signal (i.e. composite, s-video, component, etc.) coming from your PS2, then the signal resetting for Klonoa 2 should not be a problem whatsoever. It's only when your using an upscaler in conjunction with HDMI cables (i.e. Framemeister, OSSC, etc.) that the signal resetting becomes a problem. Every time Klonoa 2 loads a different area of a level, a cutscene, or load the game back up if you die, then you will see a short blackout in between these transitions when using HDMI. This is because upscalers that use HDMI convert that analog signal to a digital signal through the HDMI cord and scales up the image to a higher quality, and HDMI usually has a bit of a delay when switching between different resolutions or when the video signal has to reset. But considering you have an AV composite cable for PS2, it shouldn't be an issue for Klonoa 2 on any of your displays. But honestly man, if I were you, I would not use AV composite cables on an HD display. Trust me, those things were meant for CRT TVs and those TVs alone. I would just get component cables instead because those make the image quality look way better.
