You might be able to just pull out the SIM card from your glove box. It needs a cellular connection to share data, but without a SIM card it can’t get data.

Not sure if it has any ill effects (ie: disabling emergency response stuff) but might be worth it depending on how privacy conscious you are.

Depending on the interactivity required from the website, you can use GitHub pages. I’ve hosted my personal portfolio site/blog on there for years with no issues.

It’s limited to HTML/CSS/JS but there are also GitHub Actions to take markdown pages and render them as HTML, keeping updating the site easy for everyone.