I am computing stresses per atom. For that I have used following lines.

variable r equal 1.28 #radius of copper atom 128 Armstrong
variable vol equal (4/3)pi(r^3)
compute s_all all stress/atom # stress per atom
variable s_atom atom c_s_all / v_vol

Is this the right approach. If it is not, please elaborate, how to calculate stress per atom and volume per atom.

I am computing stresses per atom. For that I have used following lines.

variable r equal 1.28 #radius of copper
atom 128 Armstrong
variable vol equal (4/3)*pi*(r^3)
compute s_all all stress/atom # stress per atom
variable s_atom atom c_s_all / v_vol

Is this the right approach. If it is not, please elaborate, how to calculate
stress per atom and volume per atom.

volume per atom is not a well defined property. particularly not for
isolated atoms or molecular systems.
so you have to make some approximations.

for dense homogeneous bulk systems, for example, you can approximate
the volume per atom, by taking the cell volume divided by the number
of atoms (that would have the benefit of being consistent with the
computation of the total stress (and pressure) of the system).

for dense inhomogeneous bulk system, you can use voronoi tesselation
(but that is a problem for atoms at surfaces, which have oversize
volumes assigned, due to the way how voronoi tesselation works).

using a per atom volume inferred from covalent radii or similar as you
are doing above is another option.

if you dig through the mailing list archives, you should find multiple
discussions on the subject, if you need to know more.