Here's some VBA code that demonstrates one approach. The first thing to notice is that the intersection is not available as part of the profile unless you add intersection points between the two circles. Otherwise only the two whole circles are available. Once the points are added, then there are three paths within the profile and it's a matter of figuring out how the path you want is different than the other two and looking for it. The code below is using the sweep angle of the arcs to find the smaller path.
Public Sub CircleIntersectSample()
Dim partDoc As PartDocument
Set partDoc = ThisApplication.ActiveDocument
Dim partDef As PartComponentDefinition
Set partDef = partDoc.ComponentDefinition
Dim sketch As PlanarSketch
Set sketch = partDef.sketches.Add(partDef.WorkPlanes.Item(3), False)
Dim tg As TransientGeometry
Set tg = ThisApplication.TransientGeometry
' Draw the two circles.
Dim circ1 As SketchCircle
Set circ1 = sketch.SketchCircles.AddByCenterRadius(tg.CreatePoint2d(6, 0), 8)
Dim circ2 As SketchCircle
Set circ2 = sketch.SketchCircles.AddByCenterRadius(tg.CreatePoint2d(-5, 0), 7)
' Temporarily ground the circles so they don't move as the intersections are added.
Dim ground1 As GroundConstraint
Set ground1 = sketch.GeometricConstraints.AddGround(circ1)
Dim ground2 As GroundConstraint
Set ground2 = sketch.GeometricConstraints.AddGround(circ2)
' Add intersection points so the intersections are considered in the profile creation.
Dim skPnt As SketchPoint
Set skPnt = sketch.SketchPoints.Add(tg.CreatePoint2d(0, 4))
Call sketch.GeometricConstraints.AddCoincident(skPnt, circ1)
Call sketch.GeometricConstraints.AddCoincident(skPnt, circ2)
Set skPnt = sketch.SketchPoints.Add(tg.CreatePoint2d(0, -4))
Call sketch.GeometricConstraints.AddCoincident(skPnt, circ1)
Call sketch.GeometricConstraints.AddCoincident(skPnt, circ2)
' Delete the grounds.
ground1.Delete
ground2.Delete
Dim prof As Profile
Set prof = sketch.Profiles.AddForSolid()
' Find the union piece of the two circles by looking
' for a path that contains two arcs whose sweep is less
' than 180 degrees.
Dim pi As Double
pi = Atn(1) * 4
Dim path As ProfilePath
For Each path In prof
Dim arc1 As Arc2d
Set arc1 = path.Item(1).curve
If arc1.SweepAngle < pi Then
Dim arc2 As Arc2d
Set arc2 = path.Item(2).curve
If arc2.SweepAngle < pi Then
path.AddsMaterial = True
Else
path.AddsMaterial = False
End If
Else
path.AddsMaterial = False
End If
Next
Dim extDef As ExtrudeDefinition
Set extDef = partDef.Features.ExtrudeFeatures.CreateExtrudeDefinition(prof, kNewBodyOperation)
Call extDef.SetDistanceExtent(5, kPositiveExtentDirection)
Dim ext As ExtrudeFeature
Set ext = partDef.Features.ExtrudeFeatures.Add(extDef)
End Sub