I'll say plausible (though I question the extremely shallow depth...200m not 4m maybe?), though perhaps not the most likely. Earth is unique (so far at least) within our solar system with tectonic plates, so it's more than feasible to have planets lacking this plate structure.
The problem you will face is how the planet releases it's heat. On planets without plate tectonics, you get very large volcanoes as the means through which it releases its heat (Olympus Mons on mars is a good example of the size these volcanoes reach like this). I've seen a theory that applies to Venus that see's the entire planets crust 'melt' from internal heat in a 200 million year long event...I guess a melted and reformed crust might look like this?, seems like a stretch though. You basically need a planetary body that's cool enough internally that it doesn't have the need to expel this heat. Best if the planet has no moons as they tend to cause gravitational effects that stir up a planets interior causing more heat...and no tide to move the water around, leaving it the consistent depth)
Planetary bombardment might be hard to explain away as well. Though not as true today, the galaxy used to be a messy place with asteroid impacts being nearly commonplace (look at the moons bombardment history if you want an idea of the timeline there). Craters leave deep impacts and large rings (might actually explain the island presence you are going for).
Planets are never really round...they have bulges and the sort (earth has 4 I believe) and the rotation of the planet tends to redistribute water as well.
Those are the issues...lets give this a go:
My preferred explanation for such a bodies existence is an impact event that rips apart a larger planet. You have a larger, cooling body that suffers a massive impact that rips a section of the planet away. This surface section ripped off doesn't contain the same heat and pressure as the larger planet once did, so you are working with a cooler interior to start
This planet fragment (now a planet in it's own right) then undergoes a massive volcanic event releasing a magma flow that basically extends planet wide, filling in the cracks and leaving the planet coated in a volcanic crust. Should be close to round at this point.
No clue how the water got there (perhaps released with the lava), but the planets water undergoes a 'snowball earth' style effect where the planet entirely freezes over (freezing effect is easy as the sun this planet orbits can easily undergo an extended cold/dormant phase). This glacial 'covered in ice' period works to further flatten the planet by covering it in a large mass of heavy ice. Sun goes back to normal and melts everything leaving you with a world that you are looking for. It might not be quite prefect, but a few millions of years of erosion with no forces such as volcanic or tectonic activity to reshape the world should continue to flatten it out. Marine life such as coral tends to help this as well...millions of years worth of shelled life remain can also flatten out the seabed as it settles.
Not sure on how feasible this is though...comments and corrections more than welcome.