I would limit it to 1 level of "free" Striking Appearance to be safe, but also allow "bonus" Striking Apperance to match any mimic form's 'natural' Striking Apperance.
Like say your shape shifter is copying Hiddious. And he seen him unmasked. He can copy his 10 levels of Striking Appearance "Ugly", but only when copying him. It's allowable because it is not an all ways thing.
(Actuary that does depend of the writeup, since old Hiddious is no longer an official part of the CU. I seen a writeup with 10 levels of Striking Appearance "ugly", only when mask is removed, and writeup where he doesn't have any Striking Appearance at all.)
Does it make sense? Actually yes. You are copying the appearance of an ugly supervillain with a reputation of violence against beautiful things after all.
(If your doing someone like Marvel's Copycat, you'll need more then the Shapeshift power. You also need a VVP which only mimic the natural powers of the target mimicked.)