Yes you can! The .zip file you get from exporting the save data from the web version, you can replace some of the files with ones in the Saves folder in the Windows version, and then import the .zip folder with the copied over files.
I downloaded the new update, but every time I try opening the game an error pops up that says "Windows cannot access the specified device, path, or file. You may not have the appropriate permissions to access the item." and then the .exe file vanishes.