It is a good thing you want to do.
Thing is, no one will really be able to give you good advice unless they know your neighbor. I can only give you suggestions of what I would want you to do if I was your neighbor.
The grieving process is fucked up and people deal with it many different ways and there is no play book.
It is very possible that you attempting to celebrate his dead son’s birthday may only shove it all back into his life.
If I was your neighbor I would want you to leave it be and maintain the same boundaries we have now.