The major issue would be the fonts and typography. It’s all manual work, unfortunately.
I would suggest you make a reserve copy and start with simply replacing styles and scripts and styles.
Then using the example – https://designmodo.com/slides/app/preview/example/typography/ you can pick the correct font size and replace all classes (huge, tiny, micro, ultraBold, etc) with new ones (small, smaller, smallest, large, larger, largest, etc).
Then, if you want to improve your loading speed you can replace <iframe src=”…”> with <iframe data-src=””> for all your popups, if you have any. Then update jquery, and move all styles and scripts to the bottom of the page before </body>. This will increasingly fasten your website loading speed for google pagespeed analytics, which could drastically change your position in google search results. But that means that a second or two people will see unstyled elements, which you can hide manually with custom styles, placed in the bottom of the <head> section:
<style>
html:not(.page-loaded) svg, html:not(.page-loaded) nav, html:not(.page-loaded) img, html:not(.page-loaded) .popup, html:not(.page-loaded) .dropdown, html:not(.page-loaded) .material-icons {display:none;}
</style>
Everything else should work as usual.