Will not wear

I think it is also permissible to remove it completely, as long as it is not done to resemble women. See here:
https://www.kipa.co.il/%D7%A9%D7%90%D7%9C-%D7%90%D7%AA-%D7%94%D7%A8%D7%91/%D7%94%D7%95%D7%A8%D7%93%D7%AA-%D7%A9%D7%99%D7%A2%D7%A8-%D7%9C%D7%92%D7%91%D7%A8%D7%99%D7%9D/