To make the salmon filling: In a medium skillet, combine the cooked salmon, sake (if desired), and salt. Cook over medium heat, stirring occasionally, until the salmon easily breaks into flakes, 1 to 2 minutes. Remove from the heat and set aside or refrigerate.
To make the tuna mayo: In a medium bowl, add the drained tuna and use your hands or a fork to break it into fine flakes. Mix in the mayonnaise, soy sauce, and salt until combined. Set aside or refrigerate.
To make the rice: Place the rice in a fine-mesh sieve and rinse under cold water until the water runs clear, about 2 minutes. Follow package instructions for cooking the rice, making sure to let the rice rest with the lid on for at least 15 minutes after cooking.
Transfer the rice to a large bowl. Once the rice is cool enough to touch, make the rice balls: Scoop 1/4 cup of it into your hand, create a well in the center of the rice, and add about 2 tablespoons of the salmon filling or tuna mayo. Press 1/4 cup of the rice over the filling to seal it in. Wrap the rice ball with a strip of nori. Repeat with the remaining rice, fillings, and nori. Serve immediately, or refrigerate for up to 2 days.