Are there seamounts as close as 100 m to the water surface and not inside any Exclusive Economic Zone?
Yes, there are many. According to the seafloor topographic data of ETOPO (1 arc second resolution), and the Exclusive Economic Zones (EEZ) database of marineregions.org. There are at least 157 seafloor features higher than -100 m (closer than 100 m to the sea surface). With that data, I made the following figure that shows:


ETOPO topographic data
All EEZ polygons
All 157 -100 m contour lines that are completely or partially outside any EEZ.
A red point at the centroid of each contour line (to make even the smaller seamounts visible).




Some of them are just a few meters below sea level according to ETOPO.

But note that with this data we can only see large features. ETOPO resolution is about 2 km. Therefore, a seamount with a sharp summit just above -100 m would probably not show up on ETOPO data.

For more information about individual seamounts you can query the Seamount Catalog of EarthRef.org. There you can find high resolution multibeam seafloor topographic data for many seamounts, there are more than 1,800 seamounts in the catalog so far.

For example, for Vema seamount that was mention by @arkaia and that corresponds to the point just West of South Africa in my figure, you can find data like this: