What are your thoughts on hair system/ hair patch ?

I’ve been married for 8 months now and have known this woman for more than a year. We get along very well but I have been insecure and embarrassed to tell my wife that I wear a hair system to cover my hair loss. It’s weighing me down with fear every day about what would happen if I told her. I am thinking of telling her in 2 days during our quiet time together. I’m extremely nervous and scared about how she would take the news. Is it a big deal for women to find their partner wearing a hair system/wig ?