I'm not really interested in learning a big "frameworkd" just so I can use a mini-package that only implements part of it

That's not really the case here... Mojolicious::Lite is part of the Mojolicious distribution, and instead of only implementing "parts" of the full framework, it just makes the full framework easier to use to write small applications. See Mojolicious::Guides::Tutorial.

I don't remember how any more so I might swing towards ::SIMPLE and let it handle the headers and such.

Note that the HTTP headers are quite different from HTML generation, and it's usually a good idea to use a module to handle the HTTP headers. As for HTML generation, you might be interested in HTML::Tiny, as mentioned in CGI::Alternatives, if you want to go that route instead of using a templating engine such as Template::Toolkit.