The cornbread is probably uncritical, but double-check your recipe for the chocolate cake:
If it is a "mix-all-dry-ingredients / mix-wet-ingredients / combine-and-bake" type of cake (like for muffins), you are ok. But if the cake requires creaming butter and/or eggs with sugar and folding in cocoa and flour at the end, you are in trouble if you dump everything in one bag. (Two or three bags might work, depending on the recipe steps.)
Apart from that, your dry ingredients stay safe if they stay dry. Any humidity can lead to lumps or the baking powder activating prematurely and thus flat cakes.
So keep your mixes in airtight containers and you are good to go.
A few practical tips:
You might want to take a few extra materials with you - like flour or cocoa to dust your pan or extra flour if you need to shape or roll the dough. Confectioners sugar or cocoa can come handy for a quick dusting should you need to hide a few, ahem, cosmetic flaws.
Not all ovens are callibrated well, so if you have a separate oven thermometer, take it with you. Also, keep an eye on your product while it is baking, you might have to adjust baking time or temperature (elevation!) a bit.
Your dry ingredients may settle during transport, aerating them helps a lot for better results. Either sift them or stir with a wire whisk.