How about no cake????
I have been doing parties for my kids forever and it seems like they never eat, they play, play, play. If you prepare a nice lunch with cut up vegetables, fuit, and pieces of interesting proteins, they will be satisfied. Make homemade "pop/soda" from selzer water and juice and everyone will be happy.
We usually sing Happy Birthday before present opening and the candles on the cake aren't missed. Just think a birthday party where no one throws up!!!