Change combobox drop down list border color in C#

Is it possible to change the border color of a combobox dropdown list in c#?

I want to change the white border to a darker shade to match the dark scheme. I searched through the .net documentation and found the DropDownList.BorderStyle property. However, I'm not sure if this will work. I am using WinForms.

Here is the class I'm using for the combobox:

public class FlattenCombo : ComboBox
{
    private Brush BorderBrush = new SolidBrush(SystemColors.WindowFrame);
    private Brush ArrowBrush = new SolidBrush(SystemColors.ControlText);
    private Brush DropButtonBrush = new SolidBrush(SystemColors.Control);

    private Color _borderColor = Color.Black;
    private ButtonBorderStyle _borderStyle = ButtonBorderStyle.Solid;
    private static int WM_PAINT = 0x000F; 

    private Color _ButtonColor = SystemColors.Control;

    public Color ButtonColor
    {
        get { return _ButtonColor; }
        set
        {
            _ButtonColor = value;
            DropButtonBrush = new SolidBrush(this.ButtonColor);
            this.Invalidate();
        }
    }

    protected override void WndProc(ref Message m)
    {
        base.WndProc(ref m);

        switch (m.Msg)
        {
            case 0xf:
                Graphics g = this.CreateGraphics();
                Pen p = new Pen(Color.Black);
                g.FillRectangle(BorderBrush, this.ClientRectangle);

                //Draw the background of the dropdown button
                Rectangle rect = new Rectangle(this.Width - 17, 0, 17, this.Height);
                g.FillRectangle(DropButtonBrush, rect);

                //Create the path for the arrow
                System.Drawing.Drawing2D.GraphicsPath pth = new System.Drawing.Drawing2D.GraphicsPath();
                PointF TopLeft = new PointF(this.Width - 13, (this.Height - 5) / 2);
                PointF TopRight = new PointF(this.Width - 6, (this.Height - 5) / 2);
                PointF Bottom = new PointF(this.Width - 9, (this.Height + 2) / 2);
                pth.AddLine(TopLeft, TopRight);
                pth.AddLine(TopRight, Bottom);

                g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.HighQuality;

                //Determine the arrow's color.
                if (this.DroppedDown)
                {
                    ArrowBrush = new SolidBrush(SystemColors.HighlightText);
                }
                else
                {
                    ArrowBrush = new SolidBrush(SystemColors.ControlText);
                }

                //Draw the arrow
                g.FillPath(ArrowBrush, pth);

                break;
            default:
                break;
        }
    }

    [Category("Appearance")]
    public Color BorderColor
    {
        get { return _borderColor; }
        set
        {
            _borderColor = value;
            Invalidate(); // causes control to be redrawn
        }
    }

    [Category("Appearance")]
    public ButtonBorderStyle BorderStyle
    {
        get { return _borderStyle; }
        set
        {
            _borderStyle = value;
            Invalidate();
        }
    }

    protected override void OnLostFocus(System.EventArgs e)
    {
        base.OnLostFocus(e);
        this.Invalidate();
    }

    protected override void OnGotFocus(System.EventArgs e)
    {
        base.OnGotFocus(e);
        this.Invalidate();
    }
    protected override void OnResize(EventArgs e)
    {
        base.OnResize(e);
        this.Invalidate();
    }
}