Following the link to the Carbon atom, one sees the second level of the electron orbit is the size of the first level x n2/(Z-2). Here, n = 2 and Z = 6 so this factor comes out to be 1; the atomic diameter given in the Table for Hydrogen is a good approximation for the diameter of Carbon as well.
Thus, we are taking an object that is in fact 10-10 m across and representing it with a tennis ball that is 0.06 m across. Taking ratios,
0.06/10-10 = X / 10-4 where X is the scaled up diameter of the hair.
X = 6 x 104 m - 60 kilometers wide.
At this scale, the atom is 0.06m across and the nucleus is 10-4 times this width of 6 x 10-6 m. This is 0.06 times the width of a real hair, so no, your eyes could not see the nucleus in a tennis-ball-sized atom.