Hi, I have gone through your requirement and I have seen your existing website as well, as per my understanding you want us to redesign your existing website, Thanks for sharing your existing website link, as per my understanding your existing website has been developed in Wordpress, right?
If I work on your live website mean live server then you don't have to lose the rank and don't worry If I work on your live server, everything will same and secure I am an experienced developer, I have an experienced in development more than 7+ years, I have a deep knowledge of HTML, JS, JQUERY, PHP, WORDPRESS, CSS, BOOTSTRAP, WORDPRESS, ANGULARJS, CAKEPHP, LARAVEL, SEO Many more
I have a confidant I can complete your project better than your expectation, let's connect
Regards
Dipak