why did the corporate chick wear a wig?

No she doesn't have cancer.

She had been pulling chunks of her hair out due to Homelander making her a nervous wreck and never knowing what he's gonna do, like get angry and kill her. So she began just tearing her hair out everytime she got stressed, she'd been doing it all throughout the season, even during sex she wanted her hair pulled out. Then in the finale we see she'd pulled almost all of her hair out and had been wearing a wig.