Although I understand the reasoning behind the C# vs. C Natural question, I can't find any evidence that the C# needs to be changed.
No score that I can find has it listed as a C# and I can't find any discussion about the note.
Here are a few pictures of scores I DID find--the last one is the Beethoven manuscript:
If anyone finds anything different, please let me know. For now, it stays C#.
plc