The solitary unaccented “c” is pronounced /t͡s/ (except in combinations “cz” and “ci”), so I think the proper phonetic notation would be /ɕɲaˈdet͡s.ki/ “Shnya-DETS-ki”. (I’m not Polish, but I am learning the language, and I have heard the name spoken by native Polish speakers. Also, brothers Jan and Jęndrzej Śniadecki were notable scholars in my alma mater.)
And while -ski/-cki was originally the suffix for locative surnames (mainly for landed nobility), at some point (this article says 16th century) it became basically the default identifier of Polish family names and started to be applied in all sorts of cases - for profession-based surnames, for names coming from other languages whose owners wished to appear more Polish, etc. So the specific etymology might not lead to any particular locality. Perhaps one of @Mark_Sniadecki’s ancestors was just notably swarthy.
