I know the designer of one of the responsive skins and it took a lot of time with a lot of advanced HTML5 and CSS3 knowledge just to get the appearance. It then had to be shipped to Adobe for them to make it work. That is the explanation behind the answer which is NO.
There is also the issue of sticking with Classic. It will not be developed any further and the 2020 version does not ship with a Classic option. New features will be in the new UI only and looking further down the line, it's possible there will be browser compatibility issues with Class version outputs. I can't say that definitely but it would not surprise me.
If and when you do make the change to the new UI versions, Adobe will be focussing more work on frameless outputs so I recommend considering frameless skins for your project. The calls using URLs are different so you need to discuss that with your developers if you use that method for context sensitive help.
My own view is if you want a significant change to your output, the route is to upgrade and switch to a frameless output. Many more customisation options are built in and more skins will be developed over time. It's not a five minute job but neither is doing what you want in Classic and that will have a limited life.
This page on my site will give you some idea of how many more customisation options there are.