I have used the peroxide cream on a couple items and although it did a great job of restoring the color, it was also blotchy in areas where some spots were brighter than others. You could visually see the blotchy spots when you picked it up as well. It wasnt really bad, but it wasnt uniform either.
I dont know if there is a better way to apply it, but poured out some of the cream onto the case (a Commodore VIC-20 was one of them) and, with gloves on, rubbed the cream all over the case top and sides. I then covered it with plastic wrap as best I could, trying to keep any creases in the plastic wrap to a minimum for a flat covering. Then set it in the sun for 10 hours. After that, took off the plastic wrap and cleaned off the cream.
If you watch the video for the 8-Bit Guy on Youtube where he uses the cream to restore a Roland unit, if you pause the video when he's showing the case after using the cream, you can see some of the blotchy spots I am talking about - (https://www.youtube.com/watch?v=AUvICKyXnqU - go to 7:41). Its not horribly noticeable, but its there (or the three monitors I have viewed it on are all bad).
Overall, it works OK, but I imagine putting the case in a container and filling it with Peroxide to completely cover it would make it look way better.