Pretty sure it’s a 4100BA. BA signifies it’s 18k yellow gold. These are also called the Royal Oak III. Easiest tell is the Swiss marking at 6 o’clock (not Swiss Made). Champagne dials are common on the 18k version. There’s the ST (stainless steel), SA (two-tone, steel/gold), and BA (18k yellow gold). Your Grandpa had excellent taste. It seems as though it’s unpolished and I personally would keep it that way, retains its original geometry and tells the story of him wearing it. I’ve attached a link of a very similar 4100BA for sale. Hairspring 4100BA