Geoff Swan wrote:
The OP said they wanted: "to add a contact form that allows visitors to fill in name and email and message and then send it with a button-click to my email address".
That is precisely what this example does.
Any form can be made as simple or complex as you like, they are just fields on a page. You can dress it up any way you like but the outcome is the same.
The OP also stated that they cannot use the PHP mailer, but could use SMTP, which would indicate that they may have some knowledge of simple PHP programming. It's not too late to learn if you want to make useful backends for web applications.