Why do you need to export with C2 runtime? It's not a great idea since C2 runtime will also soon be deprecated.
If you are certain you need to do this, it's possible to add old function object, I did it myself recently. I believe apart of modifying the c3proj file, you also need to copy Function.json and add at least one "on-function" block to one of the event sheets. It may be easier to create a blank event sheet for this purpose in your project.