Try hard wax in the private area. Try finding out a good salon giving hard wax service. For someone who has dense hair, this works best. There would be not much pain as compared to waxing or threading, it would be like a bee sting. Just for that moment. Take the service from am experienced person and not just anyone. Try gathering information about that person's service like, how the others clients have felt, how many sittings it would take. Be relaxed when you are talking to that person and even more relaxed when hard waxing is done. The more relaxed you are, the more easy it would be for you.

Good Luck and let us know what procedure you have followed.