If you set the form's KeyPreview property to true, the control's OnKeyDown method will be called first regardless of which control has the input focus. You can then handle the keystroke and programmtically open the dropdown.

Example:
this.KeyPreview = true;

protected override void OnKeyDown(KeyEventArgs e)
{
    if ( (e.Modifiers & Keys.Control) == Keys.Control &&
         (e.Modifiers & Keys.Shift) == Keys.Shift &&
         (e.KeyCode & Keys.E) == Keys.E )
    {
        this.ultraComboEditor1.Select();
        this.ultraComboEditor1.Editor.DropDown();
    }
       
}