There are several alternative methods to keep your cat's teeth clean without brushing. You can try changing their diet to a dry food which can help reduce plaque and tartar formation. Dental treats designed for dental hygiene can also assist in cleaning your cat's teeth. Additionally, using natural dental care products such as gels and water additives can help inhibit plaque and tartar buildup. Regular check-ups at the veterinarian and professional dental cleanings are also important for maintaining your cat's dental health.