Thank you for your response. The stylus device attached is actually a swizzle stick - often used to stir drinks. The watch was a gift to my late husband from his father, and the two of them had a pnechant for champagne with a few drops of grand marnier added - hence the need to stir!
I had been considering selling the watch on eBay, but I may reconsider and pass it on in the family. I had never heard of Vacheron & Constantin watches, and have been educated thanks to this site. I did a search of 'Merimont' and came up with one of your previous posts. I also came up with 'Merimont was a partnership between Vacheron & Constantin and the American Watch Case Co. from 1917 until 1938'.
I have added another picture. The watch is 1.75 inches in diameter and fits snugly in the palm of one's hand. It feels as if it belongs there! I might even use it myself.