Using wordpress for a four-page website may be an overkill?

I don’t think it’s overkill. IMHO even a small site can benefit from running WordPress.

World wide web is a very dynamic environment and your site should stick to this flow.

You can keep your site up to date when it comes to terms of usability, security and other standarts just by keeping your WordPress core updated.

I’d expect no troubles with speed/performance with such a small project.

And of course it is very scalable for any future client needs like Wyck has mentioned.

home, about us, services, portfolio
and contact … no
dynamic sections

In my experience often portfolio is a dynamic type of content. Your use case can be different of course.

One more thing: time spent learning how to make WP fit your needs is an investment that will come back to you ( probably during your next project 🙂