It is far easier to "refuse" to shake hands and get away with it not being seen as an "insult" if your hands are full.
If your brother had been juggling the baby, the diaper bag, and anything else that he could carry to make things easier for the baby's mother......then uncle would have come across as the ONLY rude one because you just don't risk dropping a baby to shake hands.....this works best if the baby is a squirmy one that takes both hands to keep a good, firm grip on.
But even a limp, sleeping baby might need both hands if you have a blanket on one shoulder, a diaper bag, the baby, a pacifier, a stuffed animal trying to fall out of the diaper bag, and.....well, you get the idea - keep your hands obviously too full to have one to spare to shake hands.
Too late for the christening and after-party - but something an Aspie can remember as a "rule".
If you don't want to shake hands or get screamed at for not shaking their hands - have your hands full of something that is obviously too precious to risk dropping. No baby? He can carry any leftovers in glass dishes out to the car for his wife (spouse, partner, whatever) - he can hold onto the toddler (babies do grow up - but they sometimes have to be carried out to a vehicle while asleep - and this is another good technique to avoid shaking hands without being too obvious) and carry something else in the other hand (keys, a purse, diaper bag for a younger sibling, Christmas stocking if they've just been over for the family get-together, that sort of thing).
Or he can mention having a "sore hand", if he can pull off the social lie/little white lie without being obviously telling a lie. Some can, some can't.....wearing an elastic brace or a strategically placed bandage of some kind helps keep some of the worst "I'm gonna shake your hand and squeeze it till it hurts to show how sincere I am" types (or is that "I'm gonna squeeze it till it hurts to prove that I am stronger than you are or superordinate to you"? I'm never sure....).
I had to read an article about "body language" in high school to realize that I'd been missing something that everyone else thought was obvious. I went into sociology because "science" and "engineering" make sense - I wanted to study what I didn't understand - which was how people interact. After reaching my fifties, I understand people much better....some of the time.....I just don't understand all of the people all of the time. Apparently logic circuits got left out of a lot of people - I'm still trying to figure out which ones, because the logical ones don't have pointed ears....and the illogical ones don't look obviously Klingon...or like trolls, orcs, sprites, or anything else that would help me tell them at a glance from the logical ones.
But I digress...and your brother might have been a 1 on a rudeness scale of one to five - uncle reached a 5 and was apparently trying to scream his way to a 6, even if the scale wasn't meant to go that high.