So, I really want to - as my very first proper speed-run - do Slender the Arrival: Anniversary.

The thing is, I hate, HATE, Controller on that game.

Now it does support Keyboard and Mouse, controller prompts still appear though.

Would that be disqualified?

MKB is just a different way to control the game. There's typically no requirement saying you must do runs with controller especially on PC games so you should be fine. If you're really concerned, you can double check with the mods but more than likely they'll just say there's no issues with it.