I think Mario Kart games are considered "Mario games" but being in its own genre and with multiple entries, it would certainly be fair to call it a separate series as well. Even games with the same genre (such as Super Mario RPG, Paper Mario, Mario & Luigi) could be considered separate series from each other based on the narrative or engine (though the upcoming Mario & Luigi: Paper Jam converges them, but could just be a once-off or occasional crossover while retaining their "seriesness"). When counting the main Mario games, I always used to lump all the games prior to the "New" series together, but when I think about it, aren't Super Mario 64, Sunshine, Galaxy and Galaxy 2 really in their own series? Instead of one "main" Mario platforming series there could be two or three. And then there are the Donkey Kong, Yoshi, and Wario games. Some have Mario, but most now do not, and are now fairly distinct. So it's really about how you want to distinguish them, after all, it's your wall!
My opinion: if you count Mario Kart, you'd probably be pressed to include other Mario spin-offs, like Mario Tennis, Mario Golf, Mario Party, etc. But then it will get really really big. That'd probably be the best justification for separating each series.
I see you said you don't count the Zelda CD-i games - fair enough, there's enough of a case to disavow them. I don't think anyone would complain if you added the Tingle games if you wanted to bulk up your Zelda display. It's not like there are many. If Tingle gets a dozen entries which have no Link or Zelda at all, then you might consider splitting them.