Crazy question: is it 100% required to use a mixer for chocolate cake?

I use this thing called a SPOON for all my baking:)
(except for meringue cookies) There is no such thing as a stand mixer in my kitchen.

Checking the recipe for Perfect Chocolate Cake, I would say that yes, absolutely, you can make this without a mixer of any kind. I would use two bowls, however. I'd whisk all the dry ingredients together in a big bowl. Then, I'd whisk all of the other cake ingredients except the boiling water in a separate bowl. I'd then add the wet ingredients to the dry ingredients and whisk well and then add the boiling water. Blending the wet ingredients together first will make it easier to blend the wet and dry ingredients together.
I'd also add that this is not a crazy question at all! I'm sure others out there will also want to know, and will be grateful that you asked. ;o)

Three answers -
if you are making a recipe that creams butter and sugar, a mixer is helpful but not required;
if you are making a recipe that uses oil, you can mix by hand using a whisk or spatula;
if you are making a refrigerator chocolate cake, no mixer is required, it's very easy and results are delicious.
Have a good dinner party!
Here's an example, from a very fine UK cooking teacher, cookbook author and one of the original judges of The Great British Bake Off.
https://www.tfrecipes.com/mary-berry-chocolate-biscuit-cake/