Is there any way you know of to add a custom/extra field to just a single category and not all articles as described here, without using an extension like k2?
While it may not be what you're looking for, you could use the Fields Attach component. It's not a CCK like K2, it extends the built in articles and gives you custom fields. It supports having the fields appear only in the editor for articles in certain categories, which is what you're trying to do.
Without spending much thought on your requirement, I can't imagine an easy workable custom solution to your problem.
Thinking that you are going to need a way to manage the extra field(s), and also a way to check for the categories (probably with a plugin (??))..
But unless you want to get your hands dirty with code, why to re-invent the wheel?
Since someone else have considered and provided a solution for this kind of problem, I think that this is the case where is better to consider a 3rd party extension, which will provide you with what you need.
Fields Attach comes really handy in your particular situation. It will let you extend Joomla's core content, with your desire custom fields. It provides most of the common field-types and you can create fields-groups and assign them only to specific categories.
Of course, you can also try with other CCK extensions, that will let you build your own content-items.