There shouldn't be an issue, you can just download the new version then start playing with the old save. The 0.4 should find it automatically. Ren'py does saves in two places, one in the game folder and the other outside it. If you are worried don't delete the old version until you know the new version can find the save data.
Worst case: Go into 0.3 Game folder and you will see a folder named Saves. Move that into the 0.4 Game folder.
But again, it should just work without doing anything. No worries.