You can stir a White Russian or not. It's totally up to you. You could even shake it with ice in a cocktail shaker if you wanted to. When shaking with ice, it slightly whips the cream making it feel extra luscious in your mouth. I say give it a try and see if you prefer one over the other. While there are "rules" in making cocktails, my opinion is to try things and keep doing what you like best.