Make a reduced-yellow scramble by deciding on a proportion of yellow to white, say one whole egg added to 2 egg whites. You can do this with a whole egg from a shell plus boxed whites. Use a small bowl (like a cereal bowl) and add about 1/8 cup of skim milk, then scramble vigorously with a fork for a few seconds. Microwave on high for 45 seconds. Remove from the microwave and add a little nib of butter or a few drops of olive oil. Rescramble. Microwave on high for 30 seconds. That's it! Now you just salt and pepper to taste. This may be a little runny, which is great over unbuttered toast or you can let it stand outside the microwave so that the residual heat continues to cook it to the desired state. If your microwave is not as powerful as mine, you will need to experiment with a bit more microwave time (maybe additional 10 second increments).
With the shape you're in, you shouldn't need to worry about eating some yellow. We all need some fat in our diet. Fat is essential to body chemistry, cuts down on cravings, and aids elimination.
There are other great ways to cook eggs that let you remove and discard the yellow after the cooking is done. Shell eggs are cheap enough that you can do this and still come up even with the cost of boxed whites. Email me if you want directions for steam-fried or hard boiled (yeah, there are tricks to get them perfect). Hard boiled whites are super when chopped and added to tuna salad. Active dogs need eggs for their coat (maybe 2 per week), so you could share a cooked yellow occasionally with your canine bud, provided that you are being careful about avoiding fat from table scraps, etc. .