People don’t usually go up to people they barely know and ask them if they are OK unless there is evidence that suggests that the person is not okay, and it might be due to something the person can control, such as the temperature of the room, offering of a seat, adjusting of the blinds, or providing directions to the facilities. If you are talking about people who are close to your such as a nosy mom or sister, then you can use whatever more polite substitute for “mind your business” you prefer.
However, if you find that people you barely know are frequently wondering if you suffer from chronic constipation, you may want to consider that your public disposition is unpleasant. It’s not usually necessary to “plaster a fake smile” to avoid being asking if you are “okay” on a constant basis. However, people feel uncomfortable if someone is scowling at them and they can’t figure out why. They become insecure. They wonder if their breath stinks. They wonder if you don’t like their shirt. They begin to worry if they are inadequate to you in some way.
Lots of people are not fully aware of how much disgust shows on their face. My husband is one of them. When he is not engaged in anything particular and his mind travels to something he disapproves of, he stands there in full view of the public with an expression of contempt on his face that gives anyone who approaches him the impression that he thinks they are literally composed of dog droppings. He has to be careful about this when in the work place, where this is unacceptable. He also has had to be apologetic about this in more casual environments and confess to people that it isn’t personal. He was just thinking about selfie sticks and how much he hates them.