I would recommend you to write directly to The State archive of Poltava region. Here is the link to their Internet site. Unfortunately they have contact page in English only http://poltava.archives.gov.ua/en/page/contactshttp://poltava.archives.gov.ua/en/page/contacts
In your request letter you should provide your full name and post address and e-mail. As far as Stefan was born in Austria he most probably was catholic or lutheran so archive specialists should look for metric books of Catholic or Lutheran churchs of Poltava.
If you wish I can translate your request to Russian (all Ukrainians read and speak Russian) but am not sure if it will be good in such political situation