You are right in thinking that a thin walled pin will fail primarily by compression/wall buckling (I tend to think about more as crushing), however that does not change the calculation of the shear stress.
Shear stress is defined in a very specific way: by dividing Forces acting on a direction parallel to a surface, divided by the surface area.
Of course that increases when considering shear stress which are induced due to bending depending on the cross-sections, or because of stress concentrations (see here https://www.fracturemechanics.org/hole.html). Despite these cases (and maybe some other I am forgetting) where the nominal shear stress is factored, the baseline calculation of shear stress remains the same.
If you want to understand failure, you'd consider all types of stress (normal and shear stresses) and the use some failure theory (Tresca, Von Mises etc) to determine if failure occurs. If you are worried about buckling you'd need to carry out a different type of analysis.