You could trap the mouse move messages, and move the form based on the net movement of the mouse. An easy way to achieve the same result is to make Windows believe the caption bar was clicked on by trapping and modifying the WM_NCHITTEST message.

Example:
type
  TForm  = class(TForm)
  private
    { Private declarations }
  public
    procedure WMNCHitTest(var M: TWMNCHitTest); 
      message WM_NCHITTEST;
    { Public declarations }
  end;
var
  Form : TForm ;
implementation
{$R *.DFM}
procedure TForm .WMNCHitTest(var M: TWMNCHitTest);
begin
  inherited;
 {If the client has been clicked, make Windows believe}
 {it was the caption bar that was clicked on}
  if  M.Result = htClient then
    M.Result := htCaption;
end;