A couple of things to think about.
You have oranges. Use them. They are a wholefood. They are a wholefood source of carbohydrates. As they are not a packaged industrial processed food, you are on a win. If they are from your garden then it is likely that you know what went into producing them.
In a cake the problems come from the refined flour and refined sugar (including in frosting or icing). That area of cake deconstructionism would be the more interesting thing to look at. Is there yogurt in the recipe.
The way to deal with extra sugars in fruit for a keto-practitioner is fermentation. Let the bacteria and yeast predigest those sugars before they go inside the low carb eating human.
It’s a birthday. A downside of following a strict ketogenic regimen is the social impacts on the keto practitioner’s psychology. I think it is OK to make the cake. If you want to eat a piece of cake, do that as well. Wholefood, home grown orange birthday cake is a once-a-year food.