Two hands for me as well. As mentioned above I do left and right symmetrically. On the chin I mostly use only the right hand and do not attempt to switch hands for NS or SN passes but for EW and WE passes I do switch.

Why? Some of the contortions required to shave everything with the same hand seemed excessive and were at lest as unnatural feeling as switching hands. With practice, the left hand is much better than at first.