If the hair removal cream doesn't say it's to be used for or is safe to use on private parts then I would not recommend using those hair removal creams on your private parts because it could cause a chemical burn in your private area.
Your private areas are more sensitive than other parts of your body so if you want to use hair removal cream on your private parts you should get hair removal cream made specifically for the private areas.
Or just use shaving cream and shave the private areas to avoid any chemical burns.