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I want to totally disable a website – is altering of A and CNAME DNS records a good idea? [closed]

My wife has asked me to disable her website. She doesn’t need it. However she still wants to use her G Suite e-mail address under the same domain as website I’m going to shutdown.

So the website is on a shared hosting provider but all DNS records are managed via Cloudflare.

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I’ve blurred the domain name and also hosting IP and host. My question – is this a proper way to simply alter / or delete A and CNAME DNS records? When people type her website address I want people to see browser’s info that server cannot be found but I want to leave MX records intact.

I’ve already removed public_html and all domain data from the shared hosting. Now when I enter her site it shows hosting’s 404 template. Should I proceed with A and CNAME?