When an HTTP proxy is used, there is no way to customize the headers in the initial CONNECT request. In some situations, a HTTP proxy may require certain User-Agents or other headers. golang added support for this in net/http in 1.8. The golang issue is documented here with support added in 1.8 as documented here.

Note, this is not the same as providing a requestHeader to Conn.NewClient or Dialer.Dial. These headers are only present after the initial CONNECT request to the HTTP proxy.