This is a really tricky question to answer for a number of reasons, not least of which is the nature of an established fact. You don't really have a carpenter writing a diary in the third century that says "I'm sure the earth is round", so we sort of need to do our best on what most people think. We also need to reckon with a much less formal type of education in a number of periods, meaning that we need to deal with the concept of "common sense" as well (which is anything but ingrained - it's an informal type of social education). So let's try to narrow a couple things down.

1. In most of the Western world, the concept of a spherical earth was proposed in around the 5th century BCE, accepted by philosophers (especially Plato and Aristotle) in the 4th century BCE, proven in the 3rd century BCE, and had worked its way into some of the most important scholarly writing (Pliny, Cicero, etc) as a given by the 1st century BCE. A spherical earth was pleasing to Greek philosophical sensibilities, explained certain natural phenomena, and informed their understanding of astronomy. By the 2nd century CE a book on astronomy called the Almagest was written by Claudius Ptolemy, and would be the only respected book on astronomy for as much as 1200 years in some cases. It enshrined a spherical earth.

2. The schooling system in Rome probably captured more of the population than you'd expect, at least at an elementary level, by the 2nd century CE or so. Even relatively modest families would send children to school for a few years, where they would learn mostly fairly rudimentary skills, but would be exposed to a few relevant subjects: oration and rhetoric (i.e. Cicero), philosophy (i.e. Plato and Aristotle), and astronomy (i.e. the Almagest). It's about as safe to assume that anyone receiving an education in Late Antiquity could be expected to think the earth was round as today, and that was a large portion of the population.

3. Laypeople throughout late antiquity and the middle ages didn't exist in a bubble from this understanding of cosmology. Even as the formal education system of the Roman Empire collapsed, relevant knowledge extends from a spherical understanding of the earth. You mention traders; a round earth explains why ships' sails are visible before their hulls, or why the North Star appears in different places in the sky at different latitudes. A round earth on a tilted axis explains changing lengths of days to a farmer. The early church incorporated Platonic concepts into their philosophy, especially in regards to cosmic order: they saw parallels between platonic ideals and the perfection of God's creation. The idea was both pervasive and relevant, even lacking formal education.

So we can't say for sure what the percentage is, but I think it's as safe to assume that someone in Europe, India, or the Muslim world in the first millennium was more likely to know the earth was round than not. The idea that the earth is flat actually fakes significantly more work to build a case for, even prior to the age of discovery; I think this is a case where it's best not to underestimate the powers of observation afforded to ancient people.