The idea behind folding in egg whites is to keep the air and fluffiness from beating them. Stirring in the beaten egg whites would reverse all the hard work you just put in.
Take a spatula and fold half of the mixture over on top of the other half. Continue to fold over only until the point that the egg whites have been combined into the other ingredients. Make sure not to stir or to use an electric whisk. This will ensure that your food stays light and fluffy.