Preheat oven to 350 degrees. Stack wonton wrappers and, using a 2 1/2-inch round cookie cutter, cut into rounds. Working with 3 rounds at a time (and keeping the remaining covered with a damp towel), spread them out on a work surface; brush one side of each wrapper with oil.
Tuck rounds into nonstick mini-muffin cups, oiled side up; press down to fit into bottom and sides. Bake until golden brown, 8 to 10 minutes. Cool slightly before removing.
In a small bowl, mix cream cheese, chutney, and mustard. Spoon about 2 teaspoons cream-cheese mixture into each cup; garnish with chives, if desired, and walnut pieces. Serve.