Can I use egg whites for the whole eggs called for ...

No, I would not suggest it as egg yolks have a binding property that whites do not have.  If you want to make a healthier recipe, you can replace any oil with apple sauce and that works really well.

You can; I have. Your cake will not rise as high.

If the cake calls for 2 eggs, try 1 whole egg and 2 egg whites - practice before you try this for company. ;)

Replacing the oil with applesauce will also make a flatter cake.

Angel food cake has no fat - just an aside. Here's a good healthy recipe - a box of Angel Food cake mix (personal preference for me - Duncan Hines) and a can of crushed pineapple in its own juice -not the short tuna looking can - mix together and bake at 350º for approximately 30 minutes.

I would think if you added an extra egg white it might make the cake may be moister than using the exact amount of egg whites.

yes

My brother was diagnosed with cholesterol problems in his late 20's and began doing everything the doctors prescribed i.e., careful diet, exercise and necessary meds.  His wife immediately started cooking low or no cholesterol and our family followed suite for holidays and occasions when we are all together.  I have since always made his favorite cake egg-yolk free by adding an extra egg white for the yolks I leave out of the 2-egg recipe.  I also eliminate the fatty buttermilk with the substitute of vinegar and 1% milk.  The cake has never been dry -- in fact it is very moist but I check with a touch test at least 10 minutes short of the suggested baking time and then with a paring knife inserted in the center every couple of minutes thereafter.  I remove the cake from the oven when there is a crumb or two and a moist sheen on the knife blade.  Another source for yolk free cakes is to use an egg substitute product such as "Egg Beaters" which can be found in small cartons with the regular eggs, butter, etc. in your grocery or supermarket.  This is in liquid form and the measurements per egg is on the carton.  When skillet cooked there is really no difference in the taste compared to regular scrambled eggs.  Happy Baking!!