My son who is 5 years old has shown signs

Patient: My son who is 5 years old has shown signs of allergy to some dogs but not others.We would love to have a family pet dog but also do not want our sons health to suffer.I have done a lot of research to find out which breed would be best so we have decided upon a Cockerpoo which has very little shedding to limit the dander.Finlay symptoms have been red blotchy eyes, normally after he has thrown the ball for a dog and touched his eyes before washing his hands. He also got red itchy eyes after he laid down and cuddled up in a dog bed, a dog which moulted quite a lot.The worst was when he got licked across the face by a boxer dog, his face went red straight away with hive type stings (just like stinging nettles) after a dose of medicine he was fine.Today we met the dog we would like to buy, gorgeous 6 week old cockerpoos. They are low moulting so shouldn’t have much fur to affect Finlay’s allergy but the saliva could. As a test I wiped a tiny bit of puppy saliva onto Finlay’s face to see if it went red and blotchy, it did but cleared up with 30mins after cleaning.My question is:Will my sons allergy get better and more immune if he lived with one, if we train the dog to not lick and we clean areas exploded to saliva and wash hands regularly will my sons health be affected?Is there anything further I can do so we can one day get a dog we have always dreamed of to complete our family?