I don't know of any connection between your Martin Pekarek and my Pekarek relatives. I tried to find Corcovec on a map to see if Katherin Petras lived in the vicinity of my relatives but couldn't find it anywhere. Perhaps the name has been changed or mispelled along the way. Have you been able to locate Corcovec? If you have, you may be able to find the name of the parish and then possibly, the parish records.
This website for the Trebon archive in the Czech Republic has digitized records for South Bohemia by parish. http://digi.ceskearchivy.cz/index_main.php?doctree=1n&la...
There may also be digital archives for other areas of Bohemia. I just haven't looked into it since my family was from the Trebon region. The records are photocopies of the actual church books and can be difficult to read because they are handwritten in the old script and of course aren't in English. Though once you see the family name you will easily recognize it in other places. You should be able to find people if you know the year and location of birth, death or marriage. I found several of my ancestors this way.
You may have experience with this but if you don't and have questions, I am happy to answer any I can. If you are interested, I can also refer you to a genealogist who lives in the Czech Republic and does research and/or translation (German and Czech) for a very reasonable rate. I connected with him just before I traveled to the Czech Republic then met him there and he was very helpful.
I do more research as time allows. If I ever come across someone who may be your Martin Pekarek or Katharin Petras, I will contact you.