I don't want to say that this type of element does not exist, but I am not aware of it being formulated in commercial code.
Axisymmetric shells exist; however you have stated that there is torsional loading on this model. Default axisymmetry does not include torsion as a variable--circumferential displacements are assumed zero. Torsion introduces a fourth degree of freedom (non-zero circumferential displacement), and this must be addressed.
Some commercial codes allow axisymmetry with torsion (for membrane or continuum elements), but shell formulation is not included in this type of analysis. I don't believe that there is theoretical limitation against having shells with circumferential displacement, I just don't know of it being done.
Brad