It's your world, but...
The erosion of dry land is not the only way to dissolve minerals into water. Volcanism, geological shifts (e.g. earthquakes), saturation of the ocean bottom, and undersea erosion caused by currents can also dissolve minerals into the water.
Would the water be distilled or nearly distilled? Absolutely not. That would require no volcanism or geological activity, no silt or saturatable sea bed, and bedrock made of something like diamond that couldn't be trivially (by comparison) eroded or dissolved by water. It's important to remember that water is known as the universal solvent. It can't dissolve everything. But it comes close.
It's not just erosion. It's that the water has nowhere else to go
It's also worth remembering that oceans are salty because there's nowhere else the water can go to distribute the mineral. So-called "freshwater" lakes and rivers aren't devoid of salt. But because they have outlets, there's somewhere for the salt to go. It therefore doesn't build up. Oceans, of course, have only two outlets: evaporation and the process of charging aquifers. The former doesn't take salt or other minerals with the water and the later can't move water away from oceans fast enough to avoid mineral build-up. A world that's mostly ocean is, from this perspective, no different from Earth or a world with only 10% of its surface given over to water.
So, what's your world made of?
If there's salt in the crust, geological events like earthquakes and volcanism will put it into the water. If there's salt in or near the sea bed silt, then it will be stirred up slowly through saturation and more quickly through sea current erosion. Some kind of saturation will occur eventually, it's really just a question of what minerals are provident on your planet.
One last thing...
I wonder how long the landmass on a 90% water world would actually last. Such a world in the Goldilocks zone would have a ton of storms. Storms that would work hard to erode what little land exists and reduce it to, eventually, sea bed. Of course, on our 71% world that doesn't seem to happen because tectonic and volcanic activity builds mountains.
Why doesn't that happen on your world? Low tectonic and volcanic activity would suggest either a whomping thick crust or a cold core. Now you have me wondering if a 90% water world can even exist.
OK, really, just one last thing...
One thing you could do. A world with that much water cover would have more evaporation and, therefore, more rainfall. I don't know if the science would allow it (my gut tells me it probably wouldn't), but suspension of disbelief could be that the rainfall is constant enough to create a freshwater layer on top of the saline layer. It shouldn't be very thick. Let's call it 3-6 meters. But such a world description wouldn't make me raise my eyebrows when I read about it.