Please reconsider the use of medication, surgery or radioiodine treatment. I am part of a hyperthyroid cat group on Yahoo and I have yet to hear of anyone successfully treating their cat with alternative medication. Hyperthyroidism is usually caused by a "benign" growth on the thyroid causing the thyroid to produce too much of its hormones. Medication treats the symptoms by reducing the amount of thyroid hormone in the blood stream. Surgery and radioiodine (I-131) therapy act by removing/destroying the tumor itself.
Excessive thyroid hormone can cause several other problems if left alone, including cardiomyopathy or cardiomegaly (thickening of the heart muscle so that it doesn't pump blood as well), high blood pressure, kidney damage, and break down of muscle tissue throughout the body. Untreated hyperthyroidism can cause a cat to lose weight very quickly, especially if the thyroid levels are very high. My cat was unmedicated for two months last summer (he had undergone I-131 treatment and it was unsuccessful for him) and he lost more than one third of his body weight (from 10.5 pounds to 7 pounds). He was all skin and bones, and being on the medication is the only reason he is alive today.