There could be a plugin, but I don’t know of one. I don’t know much about available plugins.
To custom code something, yes, you would edit a template file, but which one is theme dependent. See Template Hierarchy for an overview of what templates do what. You’ll see that if your theme does not have a category.php template, archive.php is used, if that is even available.
Even if your theme does not have a category.php template, you could create one, and it should be used for all category queries. You can see from the article that you can even create a template for a specific category term if need be.
If you were to use a generic template like archive.php, you’d need a conditional structure to only do something for category queries, something like:
if ( is_category()) {
//output category specific stuff
}
The good thing about editing templates is if you do something wrong, the worst that happens is all pages based on the template will be broken. If you were to do something wrong in plugin code, it could possibly bring down the entire site!. In general, it’s best to have a local test installation so you can fully debug code before it goes live on a production site. Or at least have a separate online test installation that’s hidden from the general public.