The mechanism for acceleration of cosmic rays in supernova remnants (SNRs) is an outstanding question in the field. We model a sample of 32 axisymmetric SNRs using the quasi-perpendicular and quasi-parallel cosmic-ray-electron (CRE) acceleration cases. The axisymmetric sample is defined to include SNRs with a double-sided, bilateral morphology, and also those with a one-sided morphology where one limb is much brighter than the other. Using a coordinate transformation technique, we insert a bubble-like model SNR into a model of the Galactic magnetic field. Since radio emission of SNRs is dominated by synchrotron emission and since this emission depends on the magnetic field and CRE distribution, we are able to simulate the SNRs emission and compare this to data. We find that the quasi-perpendicular CRE acceleration case is much more consistent with the data than the quasi-parallel CRE acceleration case, with G327.6+14.6 (SN1006) being a notable exception. We propose that SN1006 may be a case where both quasi-parallel and quasi-perpendicular acceleration are simultaneously at play in a single SNR.