Don't know what is OKEx, but I just created an account with OKX.com and they are enforcing KYC for both deposit & withdrawal. May be it is India specific as I chose country as India. Don't know the situation for old accounts.
Thanks for the information that you are facing a KYC issue on OKX. Since this thread was created to the Indian community I am going ahead and removing that exchange from the above list.
Bitfinex?
Bitfinex requires you to clear Basic Plus verification which means you would need to pass KYC.