The key point to understand here is that focal length is not a reliable indicator as to whether a lens will work well behind a dome or not.
The position of the elements within the lens body, the actual combination of lens elements used and probably a bunch of other factors in the individual lens' design are the factors that make one lens better behind a dome than any other.
The Nikon 16-35mm f/4 with a 240mm dome provide acceptable corner performance at apertures of f11 or so. (Acceptable is a personal and subjective criteria!)
By comparison, the Nikon 14-24mm f2.8, which is a much better lens, performs badly behind a dome port in general. So you will get better results from the cheaper lens.
Fisheye lenses like your Sigma 15mm create a "curved" image that tend to not show the optical flaws in the lens/dome system. Rectilinear lenses, by comparison, particularly with high resolution cameras, tend to be much more challenging optically.
Will the 20mm or 24mm work behind a 210mm dome...I did test the 20mm behind a 240mm dome (http://wetpixel.com/articles/review-nikon-fx-wide-angle-lenses) and it was not great, so I would expect it to be worse behind a smaller dome. I have not shot the 24mm, but my instinct is that it will probably suffer from similar (or worse) problems.
The best solution I have found is the Nauticam WACP with the Nikon 28-70mm f/3.5-4.5 D. This gives an effective underwater zoom range of 130° to 57°, which gives an ideal option when you need more reach. It is also corner to corner sharp at f/5.6! There is no dome port/lens combination that offers anything like this. The downside is weight/price although when you factor in the cost of the lens, a large dome and and a big extension, the latter is less of an issue!
Adam