The agency I work for allow us to choose up to three areas of the USA which we can block. I only chose my home area because it’s pretty big and I rarely travel outside of it. That lowers the risk of anyone recognising me when I’m out and about, even if it doesn’t protect me completely.
Maybe it depends on who you work for? Still, a wig or any kind of disguise sounds like a good idea, so long as it looks natural and attractive. I know some girls wear glasses with clear frames to make themselves look quite different.