"My question now: How is it possible to get myself the color from the MYSQL Table without reloading my perl document?"

AJAX. Present your page then use AJAX to call the backend (perl) to update your front end (HTML/JavaScript). If you want to make web development fun again stop using CGI (See CGI.pm HAS BEEN REMOVED FROM THE PERL CORE and CGI::Alternatives), check out Mojolicious.