Is It Still Okay To Cook And Eat Steak That Is Slightly Brown/gray On The Outside Edge?

Often steaks turn color because they sit for a day or two. If the meat smells bad, throw it out. Otherwise it has become "aged" as the blood in the meat settles to the bottom of the package and the air in the package causes the outer edges to take on a gray appearance and the meat to become pink in color. Two days of setting will cause meat to age. If this "ageing" bothers you, you can set the meat on a plate in fridge and turn it upside down every 8 hrs or so, till its used. As the blood stays in the meat, the aging slows down. Enjoy

Oxygen turns meat gray in color. It is safe if it doesn't smell bad.

If the meat is turning brown/gray that means it has been ageing and going bad. Bacteria starts growing on it, even if the steak still smells fine DON'T eat it, there could be a large chance of food poisoning.

You did not mention what do you do to keep them safe for 2 days. Probably you must have used the refrigerator. However, the problem is that change of color indicates that there is some problem with the steak. I would advise you not to eat it as there is risk of food poisoning.