Is there any natural way to reverse hyperparathyroidism without surgery?

Not Really. The only way to cure Primary Hyperparathyroidism is by surgery in most cases . But secondary Hyperparathyroidism due to chronic kidney failure can be treated medically and surgery only if medical treatment fails There is no way to cure Hyperparathyroidism naturally.
Hyperpara. You can drink a lot of water to try to prevent kidney stones. You can take drugs like Fosamax (alendronate) to try to prevent bone loss. There is a drug called sensipar which lowers calcium levels but does not prevent the bone loss. In short, if you are 41 and have primary hyperparathyroidism, you should probably have surgery. You should be seen by an endocrinologist who can refer you to a good surgeon.