There was a poster on the boards some time ago who attempted to bring a previously purchased cake into Chef Mickey's for a birthday surprise.
They were ultimately allowed to bring in the cake. However, the guest reported being VERY upset that the restaurant refused to keep the cake in the kitchen and have it brought to the table by restaurant staff as a surprise. They had to keep the cake at the table and serve it themselves as outside food was not permitted in the kitchen. The restaurant would also provide no utensils or plates for serving the cake, which wasn't that big an issue since the guests could grab plates and utensils from the buffet, but the restaurants you list are not buffets.
Yak & Yeti is not operated by Disney and might do things differently than the Disney restaurants do but it may be common for a restaurant to not allow outside food to be brought into the kitchens.
I also do not know whether there would be any issues regarding bringing a cake into the park and carrying it with you. Unless you bring a small cooler, there would likely be noplace you could safely store it.