It is possible, it seems, however I don't have experience with this.
However having a quick look through the Wordpress documentation it looks like this probably has your answer. But it does state that the article assumes you already know how to write a basic plugin and have knowledge of the Plugin API. If you don't have that knowledge, well, it's always a good time to learn!
In terms of plugins for this particular function there is one [here and [URL="http://www.laptoptips.ca/projects/tinymce-advanced/"]here and [URL="http://wordpress.org/extend/plugins/wp-super-edit/"]even here](http://www.deliciousdays.com/tinymcebuttons) which mentions buttons for css classes. I'm sure there must be more, but as you would rather do this without a plugin it may be worth writing your own if you can.
Someone else may have more knowledge of this and can probably help you more. It is definitely achievable.