WINE isn't an emulator, it's a compatibility layer. But you are correct, the WINE environment will not have your saves. If you want to play with those, you can download Ren'PY on Linux, and run the game with it via your terminal.
You can also just take the library files, and the '.sh' file, from a previous version of the game and copy them to the latest version. Just copy the folders labeled "linux-i686" and "linux-x86_64" from inside the "lib" folder of the older version and put them in the "lib" folder of the new version, then do the same with the '.sh' file.
The second method I only tested as far as loading previous saves, but I see no reason for it to fail after that. Hopefully you get some use from one of those!