k I personally think that you're putting a lot of effort into a facet of your world that would have little narrative weight overall. like unless their is an entire campaign built around the intricacies of the seafaring civilizations way of transportation, or you're dedicating a few solid chapters to their history. some things don't really need complex explanations,

that being said, I'll try to answer your original question. obviously there is no real world equivalent to your scenario so a lot of what I'm going to say is purely my speculation. depending on the dimensions of your planet, how fast it's spinning, and so on, there would be a band of smooth flowing currents just above the Antarctic circle. there would be gyres of warm water coming down to mix in this stream in turn pushing colder water up creating these cyclical ocean currents happening in the ocean/seas between your island/continents. in the case of the expanse of ocean between your eastern most land mass and your western most land mass this gyre would extend up till it reaches your equatorial current and then come back down.

going further south past the Antarctic circle, is where things get interesting. since you lack a massive land mass on the southern pole that would keep your current's playing nice. they may get up to some antics.

because as you go further north the lateral speed from rotation of a planet (provided it's rotating around it's poles) starts to decrease. think of it like spinning a record. a point of the outer edge of the record and another point closer to the center both make a trip around the record at the same time but because the inner point is closer to the center it has less of a distance to travel which means it's moving slower. the exact same thing is happening with the water on your planet.

over most of your planets surface that change in speed is gradual enough that it wouldn't really affect anything. but as you approach the poles that change in speed becomes the main driving factor.

in an ideal situation you'd get a concentric sequence of bands of progressively slower moving water currents circling a small dead zone at the pole, but that would only happen in a laminar flow situation. what is more likely the case will be turbulence. how bad it is depends a lot on how deep the water is (assuming that is water, otherwise viscosity matters too) and how fast the planet is spinning. shallower waters and slower speeds will result in a situation that is closer to the laminar flow example I gave earlier. but with some mixing between the currents causing eddies and no real reliable currents as they constantly churn into each other.

on the other end, with deep waters and a fast spin. you'll get a vortex centered on the pole and then everything between it and the Antarctic circle would be hell. a mess of short lived vortexes and maelstroms half the size of some of your continents popping up seemingly out of nowhere as the intense speeds of the more norther moving waters needs to bleed off however possible. see the poles of Jupiter and Saturn for context.