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The code below generates a plot with some ugly "fringes". Is there a way to get rid of them and get a smoother graphic?

a = 2.3;
myGray = Function[x, y, z, GrayLevel[1]];
s1 = ParametricPlot3D[0, a, 0 + x, Sqrt[1 - x^2 - y^2], y, x, y [Element] Disk[0, 0, 1], Mesh -> 21, Boxed -> False, Axes -> None, ColorFunction -> myGray, PlotPoints -> 100];
s2 = ParametricPlot3D[0, -a, 0 + x, -Sqrt[1 - x^2 - y^2], y, x, y [Element] Disk[0, 0, 1], Mesh -> 21, Boxed -> False, Axes -> None, ColorFunction -> myGray, PlotPoints -> 100];
s3 = ParametricPlot3D[0, 0, 0.8 a + x, y, Sqrt[1 - x^2 - y^2], x, y [Element] Disk[0, 0, 1], Mesh -> 21, Boxed -> False, Axes -> None, ColorFunction -> myGray, PlotPoints -> 100];
s4 = ParametricPlot3D[0, 0, -0.8 a + x, y, -Sqrt[1 - x^2 - y^2], x, y [Element] Disk[0, 0, 1], Mesh -> 21, Boxed -> False, Axes -> None, ColorFunction -> myGray, PlotPoints -> 100];
s5 = ParametricPlot3D[a, 0, 0 + Sqrt[1 - x^2 - y^2], x, y, x, y [Element] Disk[0, 0, 1], Mesh -> 21, Boxed -> False, Axes -> None, ColorFunction -> myGray, PlotPoints -> 100];
s6 = ParametricPlot3D[-a, 0, 0 + -Sqrt[1 - x^2 - y^2], x, y, x, y [Element] Disk[0, 0, 1], Mesh -> 21, Boxed -> False, Axes -> None, ColorFunction -> myGray, PlotPoints -> 100];
Show[s1, s2, s3, s4, s5, s6, PlotRange -> All, Boxed -> False, Lighting -> "Neutral", ViewPoint -> -2.1, -2.4, 1.1, ViewVertical -> 0, 0, 1]

You can restrict x and y to Disk[] using RegionFunction:

s1 = ParametricPlot3D[0, a, 0 + x, Sqrt[1 - x^2 - y^2], y, 
 x, -Pi, Pi, y, -Pi, Pi, 
 RegionFunction -> (#3^2 + #4^2 <= 1 &), Mesh -> 21, 
 Boxed -> False, 
 Axes -> None, 
 ColorFunction -> myGray, 
 PlotPoints -> 100]

Doing the same for s2 thru s6 we get

The fringes stem from the fact that the disk is discretized into a triangle mesh and its boundary edges are not very short (and the fact that $sqrt1 - r^2$ is not differentiable at the point $r =1$). You can avoid this, e.g., by using a different parameterization:

s1 = ParametricPlot3D[0, a, 0 + r Cos[t], Sqrt[1 - r^2], r Sin[t],
 r, 0, 1, t, -Pi, Pi,
 Mesh -> 21, Boxed -> False, Axes -> None, ColorFunction -> myGray, 
 PlotPoints -> 100
 ]

ImplicitRegion[] works better than Disk[] (but why?):

ParametricPlot3D[2.3, 0, 0 + Sqrt[1 - x^2 - y^2], x, y,
 x, y ∈ ImplicitRegion[x^2 + y^2 <= 1, x, y], Mesh -> 21, 
 Boxed -> False, Axes -> None, ColorFunction -> (GrayLevel[1] &), 
 PlotPoints -> 100]

Update:
Another approach is to control the discretization of the Disk[], the boundary being the most important element in this problem:

disk = BoundaryDiscretizeRegion[Disk[0, 0, 1], MaxCellMeasure -> "Length" -> 0.001];
disk = DiscretizeRegion[disk];

ParametricPlot3D[0, 2.3, 0 + x, Sqrt[1 - x^2 - y^2], y,
 x, y ∈ disk, Mesh -> 21, Boxed -> False, Axes -> None, 
 ColorFunction -> (White &), PlotRange -> All]