Hello,
Basel and WoodMart are visually similar, however, all the functionality is different. That is why you will have to do the great jot to migrate.
I would recommend you to create a staging platform where you will install WoodMart and recreate your site there, then move your ready site to live platform.
The good news is that the Header builder would easily and quickly help to recreate the header of your site. https://xtemos.com/docs/woodmart/header-builder/ And if you will need any help, you are welcome to contact and we shall suggest how to configure.
Another tool that would help you to improve your site is the template library. WoodMart has the comprehensive template library which would help you to insert ready nice templates and you will be able to build your own based on them https://xtemos.com/docs/woodmart/templates-library/
Best Regards