Updating WP 3.9 to 4.9

Hello WP community!

Long story short, I’m in charge of updating a company website that has not been touched for nearly 4 years besides posting new posts. When I started here, I was told this will be a priority coming this year and that they cannot update it without losing all of the database (I didn’t try it yet, but when they click the auto-update, it gives a warning saying that all data in the database will be lost or something). When I recommended backing up the posts, updating, and just reimporting the posts, they said no, and that they’d rather forget about it and leave it as is if that’s the case.

The current version on the site is 3.9. I read if I manually update in increments it should be fine, but this is a serious project and a huge worry for the company.

My plan was to update for each new full version, so:

Manually upgrade to 4.0 > 4.1 > 4.2 > 4.3 > 4.4 > 4.5 > 4.6 > 4.7 > 4.8 and then try the auto update again.

Thoughts? Better ways to go about it?

Thanks!