Games and goody bags are a good idea. Music depends on age of kids.
For goodness sakes, call it what it is! Birthday! if you don't you will have to explain why you are calling it 'appreciation day'. Do you want to go there on what should be a happy day? If you don't sing the birthday song it WILL be discussed among the other kids and your child will automatically be 'weird' because first they call it 'appreciation' day then they don't even sing Happy Birthday.
If you are going this far, don't make your child a target for later. Either do it up right or don't invite other kids so your child has to pay the consequences for the adults phobias.
Let the kid be a kid and have a normal birthday so someday they aren't here with stories of lame birthday parties but at least mom tried sort of thing. People do remember birthday parties their entire life.
I was recently on fb and some men were discussing another guys birthday parties from nearly 50 years ago and how much fun they had and how so & so got hurt, how funny it was, etc....yeah, I was surprised men remembered it but here they are still friends all these years later reminiscing about birthday parties.