Is it ok to spray cortaid (hydrocortisone) on the genitals after shaving?

I wouldn't : Cortaid (hydrocortisone) is a steroid & will weaken the skin with too much exposure (skin can become more sensitive, dry, tear easily, discoloration, etc) and can also make you more prone to infection including some stds. If you are itchy or irritated after shaving, your skin may be too dry (use moisturizer 6-8 hrs before shaving), razor too dull, or other irritants. Can also try switching to clippers for a while.