I think that classy and tattoos can go together. Imo, 'classy' is a clean, polished outward appearance coupled with wit (one of the best indicators of intelligence imo), charm and an affable personality.
I think classy people can have tattoos, and have tattoos that show on a regular basis. A huge skull and crossbones tattoo is not classy...because it outwardly takes away from the idea of having a friendly demeanor. While I don't know Angel personally, if I saw her out at an event, where we all had to be cleaned up and 'classy' looking, and her tattoo was showing, I would not think she was less classy for having it. In fact, depending on the dress she was wearing, her tattoo might enhance the appearance of the total package.
Tattoos are art, nothing more, nothing less. Some art is raw and graphic, some art is classy and sophisticated, and some art is crude and distasteful...and each person sees different art as different things.