Yes, 9950 is the style number and it is a Janice. There are no Janice bags that have unique serial numbers. You are right in that numbers previous to 1994 are meaningless. They are also all numeric. If you see any letters in the creed, it was made after 1994. Since your bag was made in 2002, it does have the style number in the creed as well as the date. The Dominican Republic was a give-away too, since Coach bags were all made in the US prior to 1994.
Your statement "I remember that the unique serial numbers started in 2004." makes no sense at all.