こんなんじゃだめなの？
TForm1 = class(TForm)
private
{ private 宣言 }
procedure StringGrid1MouseMove(Sender: TObject; Shift: TShiftState; X, Y: Single);

implementation
procedure TForm1.FormCreate(Sender: TObject);
begin
StringGrid1.OnMouseMove := StringGrid1MouseMove;
end;

procedure TForm1.StringGrid1MouseMove(Sender: TObject; Shift: TShiftState; X, Y: Single);
var ACol, ARow: integer;
begin
if StringGrid1.CellByPoint(X, Y, ACol, ARow) then
Edit1.Text := Format('Col:%d, Row:%d', [ACol, ARow]);
end;

カーソル下のセルを正確に取得できてるよ