I would use some spray paint...poly and shellac are not normally used for outdoor applications.
If the mirror body is plastic you may need a plastic "primer" of go with a paint designed for plastics....obviously you need to use an exterior rated paint and mask off areas you do not want to paint.
There are several auto body spray paints that you can get at your local auto supply shop exactly for what your trying to do. Do not waste your money on spray paints from big box stores if you want the finish to last.
thanks for the help. I'll check out paints at the auto parts store.