Totally ignorant of basic bike stuff. Bought the wife a cyclocross bike for Christmas. She has almost no riding experience and would like to get her used to riding clipless and get some exercise while it is snowing. I'm sure the trainer will destroy the cyclocross tires and be extra loud. Will a basic 700x23 trainer tire fit? The tires that come on the bike are 700x35c. Would like to order today while there are some good black Friday deals. Thanks.