Can non-smokers get larynx cancer?

Very rare but yes: It can happen, most often in people with long term reflux that ends up in the throat or in rare cases of people with a viral disease called laryngeal pappilomatosis.

Yes: Laryngeal cancer has a much higher incidence in smoker/alcohol drinkers. Though a non-smoker can get laryngeal cancer it is less common. Often the non-smokers with head and neck cancer often are hpv positive.

Yes but rare: The most common larynx cancer is squamous cell carcinoma. This is almost always related to tobacco use. Non smokers can get it, but it is rare. There are also other rare types of cancer that occur in the larynx that are not tobacco related.