Egg yolks and egg whites have very different roles in baking. You can almost never replace them. And in the cases in which you can, you will end up with a different texture.
In this case, it won't be sure disaster to replace, but I would be very reluctant to do it. Flourless recipes are finicky. Flour holds stuff together. Nut flours don't hold anything together, they need a binding agent. Egg whites are a good binding agent. Egg yolks are not only not good as a binding agent (except in certain circumstances, for example in custards - but you don't have this here), they are even a lubricant and as such will interfere with the binding done by the egg whites.
If you substitute here, you will not only change the taste, you risk your cookies crumbling apart in your hands.
In general, don't replace stuff in baking recipes. They are hard to design right. Even if you have some issues (e.g. allergies), it is easier to find an existing recipe without the offending ingredient than to try to tweak an existing one to work with different ingredients. Eggs are especially hard to substitute. Such a reason like "not wanting to waste" loses its sense if what you end up with is bad cookies, which are a much worse waste of products. And besides, you can do many more interesting things with a yolk than just scrambled eggs. In fact, I am frequently throwing out whites because I have found no use for them after doing something with the yolks.
If you still want to go ahead and try if the cookies work for you, try using 3 whole eggs. 2 eggs are nowhere near enough to substitute for 4 egg whites. Not only are the yolks smaller than the whites volume-wise, they will also not deliver you the binding proteins you need so badly.
Egg yolks, optionally covered with water, and in a well sealed container should hold for about 2-3 days in refrigerator.
You may also freeze them, but they require treatment with sugar or salt to prevent the proteins from turning them rubbery, at ratio of about (per the Egg Board):
- 1/8 teaspoon salt OR
- 1 1/2 teaspoons sugar or corn syrup
per 1/4 cup of egg yolks (about 4 yolks).
Of course, you then have to adjust whatever recipe you use them upon thawing to account for the sugar or salt already mixed into the yolks.
See also: Still Tasty
Best Answer
If you want soft and moist, you need egg yolks. Their emulsifier and fat content makes dough pliable, soft and smooth, and retains moisture.
Egg whites dry out a dough. This is sometimes desirable, e.g. in pate a choux. Eclairs made with whole eggs often have wet planes in the middle, resulting in an underbaked impression. If you remove some yolks from the dough and use a mixture of whole eggs and egg whites, you get a firmer, drier dough. But in many cases, people want softer, moister end products, and in such cases, recipes which increase the ratio of egg yolks to egg whites (by using more yolks than whole eggs, or yolks only) will give you a better result.