You need to found out the town of birth for your Natkaniec, since records are held at the this level.
1623 listings from a 1998 Directory of Polish names. Abbreviations are for the old provinces.>
Nazwisko Ogólna liczba Rozmieszczenie
Natkaniec 1623 Wa:23, Bs:2, BB:21, By:2, Cz:6, El:34, Gd:4, Go:1, JG:15, Kl:4, Ka:316, Ki:55, Kr:807, Ks:2, Lg:17, Lu:4, £d:10, NS:8, Op:15, Os:4, Pl:27, Pt:6, Pł:1, Po:18, Ra:7, Sd:3, Sł:25, Su:14, Sz:37, Tb:4, Ta:28, Wb:42, Wr:34, ZG:27
As you can see, yours may not come from the Krakow area.
You'll also need to bring proof that you are directly related to him
I am not sure that that is the case at the state archives. From what I understand from the Krakow Archive website you can get this info by just filling out a form if it's for genealogical purposes.
archiwum.krakow.pl/menueng.php
I could be wrong though, and it could well be you are right for the USC too.