I would be interested to know where you found all your information. Yous say Szwec is a very common surname, where? Were you speaking about derivatives of the name? I found this
http://swedishpolish.blogspot.com/There are several Polish surnames showing clearly a Swedish origin, like Szwed, Szwec, Szwen and their derivatives (root + ending) like Szwedski, Szwecki and Szwenderski, just for example. There is a long list of Swedish-Polish surnames like these, already published in this place.
1. Szwed (the largely used), which means Swedish or Swede in Polish language.
2. Szwec comes from Szwecja, which is Sweden in Polish and is a derivative of the Germanic “Schwetz” too (meaning Sweden). Polish Szwec and German Schwetz are similar pronunciations.
3. There are also Swen and Swend; Szwen and Szwend; Śwend and Swęd. They come from Sven and Svend, the popular Scandinavian names (nicknames to any Swede).
Waiting to hear from you