Personally I would rather turn the whole site into a WordPress theme. Building a custom theme really isn’t that hard and you’ll find loads of tutorials on it online. How the process usually works, and this is how I build all my custom themes, is I start building the whole site in HTML / CSS / JS and once that’s been done, I start breaking it down and building the wordpress theme using that code.
Depending on the deadline of the project, it could be a nice learning experience. Knowing how to build custom WordPress theme’s is always going to be a handy skill to have.