Cassidy does not know which course she will register for.
This is the best way to revise the sentence to avoid overly formal language. It is the one that is the closest to everyday speech. Sometimes when trying to create something less formal it is best to think about how you might hear it said among friends in a lunchroom. It is very rare for a student with his/her friends to say "for which course" or "for what course" unless it is a fragmented question. These are not common phrases found in less formal English.
I would usually use finally but that answer could change depending on the application. Go with your gut and try grammarly if you feel that finally does not work.
