Ocean currents are, in part, determined by the rotation of the Earth. The strongest currents in the equatorial parts of the Earth all run to the west, just as you would expect with a solid rotating eastward underneath. (there are also equatorial countercurrents, but you might guess from the name countercurrents that they don’t have the same strength)
On a world with no continents, shallow currents at least could be expected to follow similar patterns to atmospheric circulation. The topography of the sea floor could still be important in altering the paths of these currents, of course.
On your proposed small continent world, the orientation and angles of the coastline will be important. For example, you could expect that westward moving water north of the equator would get deflected north by the eastern edge of the continent. But what if the continent has a coastline running sharply northeast? It’s possible that the more important current in that case could be water running southward. On Earth, the major ocean basins are all surrounded by land masses that straddle the equator (Indonesia for the Pacific/Indian Ocean, Africa for the Indian/Atlantic Oceans, South America for the Atlantic/Pacific Oceans). All I can really predict about your hypothetical world is that it will have strong equatorial currents… I can’t predict whether there would be circulation around the continent or ocean basin gyres on either side of the continent (like we have on Earth) unless we know something about your hypothetical coastline.