after the button hide we can get button location and width and height to fire form click event
as follow, hope it help you
private void Form1_MouseClick(object sender, MouseEventArgs e)
{
int x=this.button1.Location.X;
int y = this.button1.Location.Y;
int w = this.button1.Width;
int h = this.button1.Height;
if(e.X>x&&e.X<x+w&&e.Y>y&&e.Y<y+h)
MessageBox.Show("clicked");
}
private void button1_Click(object sender, EventArgs e)
{
this.button1.Visible =false;
MessageBox.Show("clicked");
}