Need a theme stitcher with cookies

Problem is – i need to make a “button” to switch site design in high contrast theme for visually impaired people. And choice made must save in cookies on user PC. And it must work with links like https://www.sample.com/index.php?wptheme=WordPress+Classic so i could simply assign it to image.

I tried a bunch of plugins like Theme Switcher (didn’t work at all), and other. Any more options?