no no no .... It has to be beaten extremely rigorously to whip up the egg whites that are in the mix. this is what causes the cake to raise up so tall. I have not baked a angel food cake in a regular cake pan, however I have make cupcakes and they turned out fine. do not butter or spray the pans..this will keep the cake from raising.
By beating it with a mixer it puts air into the batter.. You can't do that with a fork no matter how hard you try. Ive baked angel food cake in a round pan before and they don't do as well as in a tube pan. They don't rise as much as other cakes do and the regular round pan is too shallow. So your cake will be flat and heavy. Maybe you have a neighbor that can lend you her mixer and a tube pan. My family loves angel food cake, and when I make one, I frost it with cool whip that has strawberries mixed in.. Sooo yummy!!
Try using a hand held wire whip. You may be able to use a large bread pan instead of a bundt cake mold. May be you could fine a used one at a yard sale cheap?
You really should us a electric mixer cause it would take forever to whisk it by hand
I would just go with what you have. I think it will still turn out ok. I have heard people dutch oven it. That would be to complicated for me though. I would just experiment, and do it and make it as easy as possible and use what you have. I am sure it will turn out ok. Good luck.