Stir coleslaw, 3 tablespoons water, salt, and pepper together in a medium microwave-safe bowl. Cover with a damp paper towel. Microwave until lightly steamed, about 1 minute and 30 seconds. Shred corned beef with hands or kitchen scissors; add to coleslaw mixture along with Swiss cheese. Stir until evenly combined.

Fill a small bowl with remaining 1/3 cup water. Lay an egg roll wrapper on a clean work surface and top with about 1/3 cup of corned beef filling. Dip your finger into a bowl of water and wet the edges of the wrapper; tightly wrap, roll, and seal. Cover egg roll with plastic wrap to prevent it from drying out and repeat this process with remaining egg roll wrappers and filling.

Heat oil over medium-high in a deep fryer or large Dutch oven until a deep-fry thermometer inserted in oil registers 350 degrees F (175 degrees C).

Working in batches, fry egg rolls until golden brown, 3 to 4 minutes, turning if necessary to ensure even browning. Let drain and cool on paper towel-lined plate or sheet tray, about 10 minutes.