Can A WordPress Theme Be Wrapped Around a Custom PHP File?

I am migrating a large website to wordpress and the final piece of the puzzle is a product info page. There is a database table of over 20,000 items, I need to continue using this table as it is shared by other processes. I have created a custom plugin that will generate links to this custom php page and this page correctly pulls the information from the DB. The problem is the style.

Is it possible to wrap a wordpress theme (header, sidebar and footer) around a separate php file (productinfo.php). I don’t need this product information to be a part of wordpress, i just need to have links to this product info and i want to make it look like its part of the website.

My end goal is to visit mywordpresssite.com/productinfo.php?ID=1 and this will load up the information and look like it is part of wordpress.