I don't think you have any concerns. A whoopie is a whoopie regardless of diameter. Most folks use 7/64 based on a 5-1 safety ratio - the rope should have a breaking strength five times your weight. The 7/64" Amsteel has a 1600 lb. breaking strength, so in your case, weighing 160 lbs., 7/64 Amsteel gives you a 10-1 safety ratio.
With 3/16" Amsteel, the breaking strength is 5400 lbs, so your safety ratio is 34-1. Your whoopies are gonna weigh a lot more than 7/64 Amsteel, but I doubt you have to worry about them breaking in your lifetime, or maybe three generations after you pass.