In a small sauce pan, combine the peaches and white wine. Bring to a simmer, cover and cook until the peaches are soft, about 10 minutes. Uncover and cook an additional 10 minutes to reduce slightly. Turn off the heat and stir in the honey, horseradish and 1/2 teaspoon salt. Using an immersion blender (or back of a fork) puree or mash the fruit slightly to create a sauce. Cool to room temperature or chill completely for later use (see Cook's Note).
Preheat a grill pan over medium-high heat.
Toss the shrimp with the olive oil and remaining 1/2 teaspoon salt. Place on the hot grill and grill until pink and opaque all the way through, about 3 minutes per side. Finish with a squeeze of lemon juice. Remove to a tray and serve alongside peach cocktail sauce.
This makes about 2 1/2 cups of sauce. It will last for up to 5 days in the refrigerator and can be used as a condiment on a cheese board or on a sandwich as well.