Oh, you have my sympathy.
My DD (now nearly 10 yo) has had a long term dog fear.
We've never been in the situation of wanting a dog, but I just wanted to be able to ho out without her running into the road. Yes it has happened 
My DS (12 yo) is the complete opposite, and he's a dog magnet. He's really good at 'reading' a dog- you know when a dog just doesn't want to say hello for whatever reason.He's fine and doesn't bother them.
What we did with DD- might or might not work:
I asked her "What's the worst the dog would do?" Strangely she's not worried about biting- it's dogs breathing on her that she finds abhorant.
I point out if the dog's on a lead, if it's wagging it's tail.
In the park (after I've taken DD to school) I'll ask owners about their dogs, and the reason why (so they don't think I'm a mad dog napper). Then I'll tell DD.So when we meet "Fido" she knows a bit about them.
She still doesn't like it if a dog comes up behind her, or round a corner but it's getting better. She'll stand in a drive rather than run.
It makes no difference if the owner says "Oh my dog loves kids" - I know they're trying to help, but I always thank them for putting the dog on a lead or calling it over.
Best thing we found is if she sees a dog from a distance a few times.Then she'll stnd next to it, but not pat it.
Then she went to a party.And they had a Staffie. He came scuttling out (as they do) to say Hi. She ducked behind me, but was ok.
Later when I collected her, the Staffie came up. She hugged him 
.
I'm not saying she's 'cured'. I don't mind if she never hugs a dog.Just that she doesn't go into one.
For a 4yo, even a little pup can be quite daunting.And puppies <strong>do</strong> mouth/bite.
If he can spend a bit of time with a staid gentle dog that would help him.