Is there really a strong need as the process is fully automated? If not, I would suggest to not spent too much time on it. Just let the user remove the header. Default exports come with a header. If it is needed, then a very simple adjustment (needs entry level Java skills) of the CSV exporter module will get you what you need.
EDIT: I just tested the CSV module and specifically the concept with the java action writeNextLine, you have full control over what you write to CSV. By default it doesn’t include a header. Did you try this module?
EDIT 2: full approach:
Indeed with the default button you will always get an header.
If you dont want this there are some modules in the market place that could help. Then you could create a custom csv or excel without or with empty headers.
This is how the microflow looks like and the other supporting microflow looks as below