If you could look directly at the North Pole from space, it would appear to spin counterclockwise. Given that spin, when a stick is placed in the ground parallel to the Earth’s axis in Egypt, the shadow cast by the stick as the Sun moves across the sky will move in a clockwise direction and a similarly placed stick in Australia would cast a shadow that moves counterclockwise.
As far back as when the ancient Egyptians and Babylonians were fashioning their first shadow clocks (~3,500 BC), the measurement of time moved in a clockwise direction. Even as more precise timekeeping methods came about, sundials (which began in earnest around 1,500 BC) remained popular throughout the middle ages and beyond, given their simplicity of construction and relative reliability. In fact, early mechanical clocks were often regularly calibrated to nearby sundials.
So, when mechanical clocks were introduced in Europe in the 14th century, their inventors were quite familiar with sundials and the clockwise direction that their shadows moved and marked time. Accordingly, by the end of that century when even cathedral clocks were sporting clock faces, they were made in imitation of their sundial forbears, with hands that moved in a clockwise direction.
The words clockwise and counterclockwise with present meaning did not appear in English until the 1870s.
The use of wise to mean a way of proceeding dates back to Old English. Clock dates to the invention of modern mechanical clocks during the 14th century. It is thought to come from either clokke (Middle Dutch), cloque (Old North French) or clocca (Medieval Latin) which all meant bell. Some of the earliest mechanical clocks were simply designed to strike a bell at set intervals, perhaps to announce prayer times or simply ring on the hour. Many early clocks did not have a face. Before they were called clocks, these early mechanical clocks were called horologia, from the Greek for “hour” (ὡρα) and “to tell” (λέγειν).
Incidentally, screws turn clockwise because our ancestors learned that right-handed people (about 80% of people) are stronger when they screw clockwise (righty tighty, lefty loosey).