Your greyhound is accustomed to wearing a muzzle. He has done so for years. The dogs should also be closely supervised during this initial period, and should not be left alone even while muzzled. Greyhounds are very adept at using their muzzles, and many a grey has been injured during dog fights even when both participants were muzzled. The muzzles should remain in place when the greys are outside until you are absolutely positive that they will get along, even when running and playing together.
Greyhounds can become VERY competitive when running together, and things can get out of hand.
It may take up to a few weeks or longer before you feel comfortable removing the muzzles outdoors. Close supervision is also a must while outdoors, both while muzzled and once the muzzles are removed. It is not always easy to know when you can consider both dogs as trustworthy. You will have to be the judge of that, based upon their behavior during the entire period. Many people feel that it is best to mix a male and a female to avoid same sex conflicts.