I have tried putting it in Basilisk and extracting it from there but when I try to open it I get an error saying the original application that made this file could not be found.
Are you saying you get this error when you try to open the .sit file in Basilisk? Classic Mac OS also relies on the Type and Creator to determine the "original application" to be launched when opening a file, so if you have a .sit file that was stored on a Windows PC, it won't know what to do with it.
You should be able to launch Stuffit Expander and then open the .sit file by using the File -> Open... command and browsing to the file's location. Alternatively, you can drag and drop the .sit file onto the Stuffit Expander icon.